parthtamu/rag-code-assistant
0
1<!DOCTYPE html>2 3<html lang="en" data-content_root="../">4 <head>5 <meta charset="utf-8" />6 <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="viewport" content="width=device-width, initial-scale=1" />7<meta property="og:title" content="random — Generate pseudo-random numbers" />8<meta property="og:type" content="website" />9<meta property="og:url" content="https://docs.python.org/3/library/random.html" />10<meta property="og:site_name" content="Python documentation" />11<meta property="og:description" content="Source code: Lib/random.py This module implements pseudo-random number generators for various distributions. For integers, there is uniform selection from a range. For sequences, there is uniform s..." />12<meta property="og:image:width" content="1146" />13<meta property="og:image:height" content="600" />14<meta property="og:image" content="https://docs.python.org/3.15/_images/social_previews/summary_library_random_a4546993.png" />15<meta property="og:image:alt" content="Source code: Lib/random.py This module implements pseudo-random number generators for various distributions. For integers, there is uniform selection from a range. For sequences, there is uniform s..." />16<meta name="description" content="Source code: Lib/random.py This module implements pseudo-random number generators for various distributions. For integers, there is uniform selection from a range. For sequences, there is uniform s..." />17<meta name="twitter:card" content="summary_large_image" />18<meta name="theme-color" content="#3776ab">19 20 <title>random — Generate pseudo-random numbers — Python 3.15.0a6 documentation</title><meta name="viewport" content="width=device-width, initial-scale=1.0">21 22 <link rel="stylesheet" type="text/css" href="../_static/pygments.css?v=b86133f3" />23 <link rel="stylesheet" type="text/css" href="../_static/classic.css?v=234b1a7c" />24 <link rel="stylesheet" type="text/css" href="../_static/pydoctheme.css?v=89a2f22a" />25 <link rel="stylesheet" type="text/css" href="../_static/profiling-sampling-visualization.css?v=0c2600ae" />26 <link id="pygments_dark_css" media="(prefers-color-scheme: dark)" rel="stylesheet" type="text/css" href="../_static/pygments_dark.css?v=5349f25f" />27 28 <script src="../_static/documentation_options.js?v=6b7c9ff5"></script>29 <script src="../_static/doctools.js?v=9bcbadda"></script>30 <script src="../_static/sphinx_highlight.js?v=dc90522c"></script>31 <script src="../_static/profiling-sampling-visualization.js?v=9811ed04"></script>32 33 <script src="../_static/sidebar.js"></script>34 35 <link rel="search" type="application/opensearchdescription+xml"36 title="Search within Python 3.15.0a6 documentation"37 href="../_static/opensearch.xml"/>38 <link rel="author" title="About these documents" href="../about.html" />39 <link rel="index" title="Index" href="../genindex.html" />40 <link rel="search" title="Search" href="../search.html" />41 <link rel="copyright" title="Copyright" href="../copyright.html" />42 <link rel="next" title="statistics — Mathematical statistics functions" href="statistics.html" />43 <link rel="prev" title="fractions — Rational numbers" href="fractions.html" />44 45 46 <script defer file-types="bz2,epub,zip" data-domain="docs.python.org" src="https://analytics.python.org/js/script.file-downloads.outbound-links.js"></script>47 48 <link rel="canonical" href="https://docs.python.org/3/library/random.html">49 50 51 52 53 <style>54 @media only screen {55 table.full-width-table {56 width: 100%;57 }58 }59 </style>60<link rel="stylesheet" href="../_static/pydoctheme_dark.css" media="(prefers-color-scheme: dark)" id="pydoctheme_dark_css">61 <link rel="shortcut icon" type="image/png" href="../_static/py.svg">62 <script type="text/javascript" src="../_static/copybutton.js"></script>63 <script type="text/javascript" src="../_static/menu.js"></script>64 <script type="text/javascript" src="../_static/search-focus.js"></script>65 <script type="text/javascript" src="../_static/themetoggle.js"></script> 66 <script type="text/javascript" src="../_static/rtd_switcher.js"></script>67 <meta name="readthedocs-addons-api-version" content="1">68 69 </head>70<body>71<div class="mobile-nav">72 <input type="checkbox" id="menuToggler" class="toggler__input" aria-controls="navigation"73 aria-pressed="false" aria-expanded="false" role="button" aria-label="Menu">74 <nav class="nav-content" role="navigation">75 <label for="menuToggler" class="toggler__label">76 <span></span>77 </label>78 <span class="nav-items-wrapper">79 <a href="https://www.python.org/" class="nav-logo">80 <img src="../_static/py.svg" alt="Python logo">81 </a>82 <span class="version_switcher_placeholder"></span>83 <form role="search" class="search" action="../search.html" method="get">84 <svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" class="search-icon">85 <path fill-rule="nonzero" fill="currentColor" d="M15.5 14h-.79l-.28-.27a6.5 6.5 0 001.48-5.34c-.47-2.78-2.79-5-5.59-5.34a6.505 6.505 0 00-7.27 7.27c.34 2.8 2.56 5.12 5.34 5.59a6.5 6.5 0 005.34-1.48l.27.28v.79l4.25 4.25c.41.41 1.08.41 1.49 0 .41-.41.41-1.08 0-1.49L15.5 14zm-6 0C7.01 14 5 11.99 5 9.5S7.01 5 9.5 5 14 7.01 14 9.5 11.99 14 9.5 14z"></path>86 </svg>87 <input placeholder="Quick search" aria-label="Quick search" type="search" name="q">88 <input type="submit" value="Go">89 </form>90 </span>91 </nav>92 <div class="menu-wrapper">93 <nav class="menu" role="navigation" aria-label="main navigation">94 <div class="language_switcher_placeholder"></div>95 96<label class="theme-selector-label">97 Theme98 <select class="theme-selector" oninput="activateTheme(this.value)">99 <option value="auto" selected>Auto</option>100 <option value="light">Light</option>101 <option value="dark">Dark</option>102 </select>103</label>104 <div>105 <h3><a href="../contents.html">Table of Contents</a></h3>106 <ul>107<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers</a><ul>108<li><a class="reference internal" href="#bookkeeping-functions">Bookkeeping functions</a></li>109<li><a class="reference internal" href="#functions-for-bytes">Functions for bytes</a></li>110<li><a class="reference internal" href="#functions-for-integers">Functions for integers</a></li>111<li><a class="reference internal" href="#functions-for-sequences">Functions for sequences</a></li>112<li><a class="reference internal" href="#discrete-distributions">Discrete distributions</a></li>113<li><a class="reference internal" href="#real-valued-distributions">Real-valued distributions</a></li>114<li><a class="reference internal" href="#alternative-generator">Alternative Generator</a></li>115<li><a class="reference internal" href="#notes-on-reproducibility">Notes on Reproducibility</a></li>116<li><a class="reference internal" href="#examples">Examples</a></li>117<li><a class="reference internal" href="#recipes">Recipes</a></li>118<li><a class="reference internal" href="#command-line-usage">Command-line usage</a></li>119<li><a class="reference internal" href="#command-line-example">Command-line example</a></li>120</ul>121</li>122</ul>123 124 </div>125 <div>126 <h4>Previous topic</h4>127 <p class="topless"><a href="fractions.html"128 title="previous chapter"><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code> — Rational numbers</a></p>129 </div>130 <div>131 <h4>Next topic</h4>132 <p class="topless"><a href="statistics.html"133 title="next chapter"><code class="xref py py-mod docutils literal notranslate"><span class="pre">statistics</span></code> — Mathematical statistics functions</a></p>134 </div>135 <script>136 document.addEventListener('DOMContentLoaded', () => {137 const title = document.querySelector('meta[property="og:title"]').content;138 const elements = document.querySelectorAll('.improvepage');139 const pageurl = window.location.href.split('?')[0];140 elements.forEach(element => {141 const url = new URL(element.href.split('?')[0].replace("-nojs", ""));142 url.searchParams.set('pagetitle', title);143 url.searchParams.set('pageurl', pageurl);144 url.searchParams.set('pagesource', "library/random.rst");145 element.href = url.toString();146 });147 });148 </script>149 <div role="note" aria-label="source link">150 <h3>This page</h3>151 <ul class="this-page-menu">152 <li><a href="../bugs.html">Report a bug</a></li>153 <li><a class="improvepage" href="../improve-page-nojs.html">Improve this page</a></li>154 <li>155 <a href="https://github.com/python/cpython/blob/main/Doc/library/random.rst?plain=1"156 rel="nofollow">Show source157 </a>158 </li>159 160 </ul>161 </div>162 </nav>163 </div>164</div>165 166 167 <div class="related" role="navigation" aria-label="Related">168 <h3>Navigation</h3>169 <ul>170 <li class="right" style="margin-right: 10px">171 <a href="../genindex.html" title="General Index"172 accesskey="I">index</a></li>173 <li class="right" >174 <a href="../py-modindex.html" title="Python Module Index"175 >modules</a> |</li>176 <li class="right" >177 <a href="statistics.html" title="statistics — Mathematical statistics functions"178 accesskey="N">next</a> |</li>179 <li class="right" >180 <a href="fractions.html" title="fractions — Rational numbers"181 accesskey="P">previous</a> |</li>182 183 <li><img src="../_static/py.svg" alt="Python logo" style="vertical-align: middle; margin-top: -1px"></li>184 <li><a href="https://www.python.org/">Python</a> »</li>185 <li class="switchers">186 <div class="language_switcher_placeholder"></div>187 <div class="version_switcher_placeholder"></div>188 </li>189 <li>190 191 </li>192 <li id="cpython-language-and-version">193 <a href="../index.html">3.15.0a6 Documentation</a> »194 </li>195 196 <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li>197 <li class="nav-item nav-item-2"><a href="numeric.html" accesskey="U">Numeric and Mathematical Modules</a> »</li>198 <li class="nav-item nav-item-this"><a href=""><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers</a></li>199 <li class="right">200 201 202 <div class="inline-search" role="search">203 <form class="inline-search" action="../search.html" method="get">204 <input placeholder="Quick search" aria-label="Quick search" type="search" name="q" id="search-box">205 <input type="submit" value="Go">206 </form>207 </div>208 |209 </li>210 <li class="right">211<label class="theme-selector-label">212 Theme213 <select class="theme-selector" oninput="activateTheme(this.value)">214 <option value="auto" selected>Auto</option>215 <option value="light">Light</option>216 <option value="dark">Dark</option>217 </select>218</label> |</li>219 220 </ul>221 </div> 222 223 <div class="document">224 <div class="documentwrapper">225 <div class="bodywrapper">226 <div class="body" role="main">227 228 <section id="module-random">229<span id="random-generate-pseudo-random-numbers"></span><h1><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers<a class="headerlink" href="#module-random" title="Link to this heading">¶</a></h1>230<p><strong>Source code:</strong> <a class="extlink-source reference external" href="https://github.com/python/cpython/tree/main/Lib/random.py">Lib/random.py</a></p>231<hr class="docutils" />232<p>This module implements pseudo-random number generators for various233distributions.</p>234<p>For integers, there is uniform selection from a range. For sequences, there is235uniform selection of a random element, a function to generate a random236permutation of a list in-place, and a function for random sampling without237replacement.</p>238<p>On the real line, there are functions to compute uniform, normal (Gaussian),239lognormal, negative exponential, gamma, and beta distributions. For generating240distributions of angles, the von Mises distribution is available.</p>241<p>Almost all module functions depend on the basic function <a class="reference internal" href="#random.random" title="random.random"><code class="xref py py-func docutils literal notranslate"><span class="pre">random()</span></code></a>, which242generates a random float uniformly in the half-open range <code class="docutils literal notranslate"><span class="pre">0.0</span> <span class="pre"><=</span> <span class="pre">X</span> <span class="pre"><</span> <span class="pre">1.0</span></code>.243Python uses the Mersenne Twister as the core generator. It produces 53-bit precision244floats and has a period of 2**19937-1. The underlying implementation in C is245both fast and threadsafe. The Mersenne Twister is one of the most extensively246tested random number generators in existence. However, being completely247deterministic, it is not suitable for all purposes, and is completely unsuitable248for cryptographic purposes.</p>249<p>The functions supplied by this module are actually bound methods of a hidden250instance of the <a class="reference internal" href="#random.Random" title="random.Random"><code class="xref py py-class docutils literal notranslate"><span class="pre">random.Random</span></code></a> class. You can instantiate your own251instances of <a class="reference internal" href="#random.Random" title="random.Random"><code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code></a> to get generators that don’t share state.</p>252<p>Class <a class="reference internal" href="#random.Random" title="random.Random"><code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code></a> can also be subclassed if you want to use a different253basic generator of your own devising: see the documentation on that class for254more details.</p>255<p>The <code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> module also provides the <a class="reference internal" href="#random.SystemRandom" title="random.SystemRandom"><code class="xref py py-class docutils literal notranslate"><span class="pre">SystemRandom</span></code></a> class which256uses the system function <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate"><span class="pre">os.urandom()</span></code></a> to generate random numbers257from sources provided by the operating system.</p>258<div class="admonition warning">259<p class="admonition-title">Warning</p>260<p>The pseudo-random generators of this module should not be used for261security purposes. For security or cryptographic uses, see the262<a class="reference internal" href="secrets.html#module-secrets" title="secrets: Generate secure random numbers for managing secrets."><code class="xref py py-mod docutils literal notranslate"><span class="pre">secrets</span></code></a> module.</p>263</div>264<div class="admonition seealso">265<p class="admonition-title">See also</p>266<p>M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally267equidistributed uniform pseudorandom number generator”, ACM Transactions on268Modeling and Computer Simulation Vol. 8, No. 1, January pp.3–30 1998.</p>269<p><a class="reference external" href="https://code.activestate.com/recipes/576707-long-period-random-number-generator/">Complementary-Multiply-with-Carry recipe</a> for a compatible alternative270random number generator with a long period and comparatively simple update271operations.</p>272</div>273<div class="admonition note">274<p class="admonition-title">Note</p>275<p>The global random number generator and instances of <a class="reference internal" href="#random.Random" title="random.Random"><code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code></a> are thread-safe.276However, in the free-threaded build, concurrent calls to the global generator or277to the same instance of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> may encounter contention and poor performance.278Consider using separate instances of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> per thread instead.</p>279</div>280<section id="bookkeeping-functions">281<h2>Bookkeeping functions<a class="headerlink" href="#bookkeeping-functions" title="Link to this heading">¶</a></h2>282<dl class="py function">283<dt class="sig sig-object py" id="random.seed">284<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">seed</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">version</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.seed" title="Link to this definition">¶</a></dt>285<dd><p>Initialize the random number generator.</p>286<p>If <em>a</em> is omitted or <code class="docutils literal notranslate"><span class="pre">None</span></code>, the current system time is used. If287randomness sources are provided by the operating system, they are used288instead of the system time (see the <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate"><span class="pre">os.urandom()</span></code></a> function for details289on availability).</p>290<p>If <em>a</em> is an int, its absolute value is used directly.</p>291<p>With version 2 (the default), a <a class="reference internal" href="stdtypes.html#str" title="str"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>, <a class="reference internal" href="stdtypes.html#bytes" title="bytes"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytes</span></code></a>, or <a class="reference internal" href="stdtypes.html#bytearray" title="bytearray"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytearray</span></code></a>292object gets converted to an <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a> and all of its bits are used.</p>293<p>With version 1 (provided for reproducing random sequences from older versions294of Python), the algorithm for <a class="reference internal" href="stdtypes.html#str" title="str"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a> and <a class="reference internal" href="stdtypes.html#bytes" title="bytes"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytes</span></code></a> generates a295narrower range of seeds.</p>296<div class="versionchanged">297<p><span class="versionmodified changed">Changed in version 3.2: </span>Moved to the version 2 scheme which uses all of the bits in a string seed.</p>298</div>299<div class="versionchanged">300<p><span class="versionmodified changed">Changed in version 3.11: </span>The <em>seed</em> must be one of the following types:301<code class="docutils literal notranslate"><span class="pre">None</span></code>, <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference internal" href="stdtypes.html#str" title="str"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>,302<a class="reference internal" href="stdtypes.html#bytes" title="bytes"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytes</span></code></a>, or <a class="reference internal" href="stdtypes.html#bytearray" title="bytearray"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytearray</span></code></a>.</p>303</div>304</dd></dl>305 306<dl class="py function">307<dt class="sig sig-object py" id="random.getstate">308<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">getstate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.getstate" title="Link to this definition">¶</a></dt>309<dd><p>Return an object capturing the current internal state of the generator. This310object can be passed to <a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-func docutils literal notranslate"><span class="pre">setstate()</span></code></a> to restore the state.</p>311</dd></dl>312 313<dl class="py function">314<dt class="sig sig-object py" id="random.setstate">315<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">setstate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">state</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.setstate" title="Link to this definition">¶</a></dt>316<dd><p><em>state</em> should have been obtained from a previous call to <a class="reference internal" href="#random.getstate" title="random.getstate"><code class="xref py py-func docutils literal notranslate"><span class="pre">getstate()</span></code></a>, and317<code class="xref py py-func docutils literal notranslate"><span class="pre">setstate()</span></code> restores the internal state of the generator to what it was at318the time <code class="xref py py-func docutils literal notranslate"><span class="pre">getstate()</span></code> was called.</p>319</dd></dl>320 321</section>322<section id="functions-for-bytes">323<h2>Functions for bytes<a class="headerlink" href="#functions-for-bytes" title="Link to this heading">¶</a></h2>324<dl class="py function">325<dt class="sig sig-object py" id="random.randbytes">326<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">randbytes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.randbytes" title="Link to this definition">¶</a></dt>327<dd><p>Generate <em>n</em> random bytes.</p>328<p>This method should not be used for generating security tokens.329Use <a class="reference internal" href="secrets.html#secrets.token_bytes" title="secrets.token_bytes"><code class="xref py py-func docutils literal notranslate"><span class="pre">secrets.token_bytes()</span></code></a> instead.</p>330<div class="versionadded">331<p><span class="versionmodified added">Added in version 3.9.</span></p>332</div>333</dd></dl>334 335</section>336<section id="functions-for-integers">337<h2>Functions for integers<a class="headerlink" href="#functions-for-integers" title="Link to this heading">¶</a></h2>338<dl class="py function">339<dt class="sig sig-object py" id="random.randrange">340<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">randrange</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">stop</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.randrange" title="Link to this definition">¶</a></dt>341<dt class="sig sig-object py">342<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">randrange</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop</span></span></em><span class="optional">[</span>, <em class="sig-param"><span class="n"><span class="pre">step</span></span></em><span class="optional">]</span><span class="sig-paren">)</span></dt>343<dd><p>Return a randomly selected element from <code class="docutils literal notranslate"><span class="pre">range(start,</span> <span class="pre">stop,</span> <span class="pre">step)</span></code>.</p>344<p>This is roughly equivalent to <code class="docutils literal notranslate"><span class="pre">choice(range(start,</span> <span class="pre">stop,</span> <span class="pre">step))</span></code> but345supports arbitrarily large ranges and is optimized for common cases.</p>346<p>The positional argument pattern matches the <a class="reference internal" href="stdtypes.html#range" title="range"><code class="xref py py-func docutils literal notranslate"><span class="pre">range()</span></code></a> function.</p>347<p>Keyword arguments should not be used because they can be interpreted348in unexpected ways. For example <code class="docutils literal notranslate"><span class="pre">randrange(start=100)</span></code> is interpreted349as <code class="docutils literal notranslate"><span class="pre">randrange(0,</span> <span class="pre">100,</span> <span class="pre">1)</span></code>.</p>350<div class="versionchanged">351<p><span class="versionmodified changed">Changed in version 3.2: </span><a class="reference internal" href="#random.randrange" title="random.randrange"><code class="xref py py-meth docutils literal notranslate"><span class="pre">randrange()</span></code></a> is more sophisticated about producing equally distributed352values. Formerly it used a style like <code class="docutils literal notranslate"><span class="pre">int(random()*n)</span></code> which could produce353slightly uneven distributions.</p>354</div>355<div class="versionchanged">356<p><span class="versionmodified changed">Changed in version 3.12: </span>Automatic conversion of non-integer types is no longer supported.357Calls such as <code class="docutils literal notranslate"><span class="pre">randrange(10.0)</span></code> and <code class="docutils literal notranslate"><span class="pre">randrange(Fraction(10,</span> <span class="pre">1))</span></code>358now raise a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a>.</p>359</div>360</dd></dl>361 362<dl class="py function">363<dt class="sig sig-object py" id="random.randint">364<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">randint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.randint" title="Link to this definition">¶</a></dt>365<dd><p>Return a random integer <em>N</em> such that <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">b</span></code>. Alias for366<code class="docutils literal notranslate"><span class="pre">randrange(a,</span> <span class="pre">b+1)</span></code>.</p>367</dd></dl>368 369<dl class="py function">370<dt class="sig sig-object py" id="random.getrandbits">371<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">getrandbits</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">k</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.getrandbits" title="Link to this definition">¶</a></dt>372<dd><p>Returns a non-negative Python integer with <em>k</em> random bits. This method373is supplied with the Mersenne Twister generator and some other generators374may also provide it as an optional part of the API. When available,375<a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><code class="xref py py-meth docutils literal notranslate"><span class="pre">getrandbits()</span></code></a> enables <a class="reference internal" href="#random.randrange" title="random.randrange"><code class="xref py py-meth docutils literal notranslate"><span class="pre">randrange()</span></code></a> to handle arbitrarily large376ranges.</p>377<div class="versionchanged">378<p><span class="versionmodified changed">Changed in version 3.9: </span>This method now accepts zero for <em>k</em>.</p>379</div>380</dd></dl>381 382</section>383<section id="functions-for-sequences">384<h2>Functions for sequences<a class="headerlink" href="#functions-for-sequences" title="Link to this heading">¶</a></h2>385<dl class="py function">386<dt class="sig sig-object py" id="random.choice">387<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">choice</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">seq</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.choice" title="Link to this definition">¶</a></dt>388<dd><p>Return a random element from the non-empty sequence <em>seq</em>. If <em>seq</em> is empty,389raises <a class="reference internal" href="exceptions.html#IndexError" title="IndexError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">IndexError</span></code></a>.</p>390</dd></dl>391 392<dl class="py function">393<dt class="sig sig-object py" id="random.choices">394<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">choices</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">population</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="keyword-only-separator o"><abbr title="Keyword-only parameters separator (PEP 3102)"><span class="pre">*</span></abbr></span></em>, <em class="sig-param"><span class="n"><span class="pre">cum_weights</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">k</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.choices" title="Link to this definition">¶</a></dt>395<dd><p>Return a <em>k</em> sized list of elements chosen from the <em>population</em> with replacement.396If the <em>population</em> is empty, raises <a class="reference internal" href="exceptions.html#IndexError" title="IndexError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">IndexError</span></code></a>.</p>397<p>If a <em>weights</em> sequence is specified, selections are made according to the398relative weights. Alternatively, if a <em>cum_weights</em> sequence is given, the399selections are made according to the cumulative weights (perhaps computed400using <a class="reference internal" href="itertools.html#itertools.accumulate" title="itertools.accumulate"><code class="xref py py-func docutils literal notranslate"><span class="pre">itertools.accumulate()</span></code></a>). For example, the relative weights401<code class="docutils literal notranslate"><span class="pre">[10,</span> <span class="pre">5,</span> <span class="pre">30,</span> <span class="pre">5]</span></code> are equivalent to the cumulative weights402<code class="docutils literal notranslate"><span class="pre">[10,</span> <span class="pre">15,</span> <span class="pre">45,</span> <span class="pre">50]</span></code>. Internally, the relative weights are converted to403cumulative weights before making selections, so supplying the cumulative404weights saves work.</p>405<p>If neither <em>weights</em> nor <em>cum_weights</em> are specified, selections are made406with equal probability. If a weights sequence is supplied, it must be407the same length as the <em>population</em> sequence. It is a <a class="reference internal" href="exceptions.html#TypeError" title="TypeError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">TypeError</span></code></a>408to specify both <em>weights</em> and <em>cum_weights</em>.</p>409<p>The <em>weights</em> or <em>cum_weights</em> can use any numeric type that interoperates410with the <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a> values returned by <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-func docutils literal notranslate"><span class="pre">random()</span></code></a> (that includes411integers, floats, and fractions but excludes decimals). Weights are assumed412to be non-negative and finite. A <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ValueError</span></code></a> is raised if all413weights are zero.</p>414<p>For a given seed, the <code class="xref py py-func docutils literal notranslate"><span class="pre">choices()</span></code> function with equal weighting415typically produces a different sequence than repeated calls to416<a class="reference internal" href="#random.choice" title="random.choice"><code class="xref py py-func docutils literal notranslate"><span class="pre">choice()</span></code></a>. The algorithm used by <code class="xref py py-func docutils literal notranslate"><span class="pre">choices()</span></code> uses floating-point417arithmetic for internal consistency and speed. The algorithm used418by <code class="xref py py-func docutils literal notranslate"><span class="pre">choice()</span></code> defaults to integer arithmetic with repeated selections419to avoid small biases from round-off error.</p>420<div class="versionadded">421<p><span class="versionmodified added">Added in version 3.6.</span></p>422</div>423<div class="versionchanged">424<p><span class="versionmodified changed">Changed in version 3.9: </span>Raises a <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ValueError</span></code></a> if all weights are zero.</p>425</div>426</dd></dl>427 428<dl class="py function">429<dt class="sig sig-object py" id="random.shuffle">430<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">shuffle</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.shuffle" title="Link to this definition">¶</a></dt>431<dd><p>Shuffle the sequence <em>x</em> in place.</p>432<p>To shuffle an immutable sequence and return a new shuffled list, use433<code class="docutils literal notranslate"><span class="pre">sample(x,</span> <span class="pre">k=len(x))</span></code> instead.</p>434<p>Note that even for small <code class="docutils literal notranslate"><span class="pre">len(x)</span></code>, the total number of permutations of <em>x</em>435can quickly grow larger than the period of most random number generators.436This implies that most permutations of a long sequence can never be437generated. For example, a sequence of length 2080 is the largest that438can fit within the period of the Mersenne Twister random number generator.</p>439<div class="versionchanged">440<p><span class="versionmodified changed">Changed in version 3.11: </span>Removed the optional parameter <em>random</em>.</p>441</div>442</dd></dl>443 444<dl class="py function">445<dt class="sig sig-object py" id="random.sample">446<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">sample</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">population</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">k</span></span></em>, <em class="sig-param"><span class="keyword-only-separator o"><abbr title="Keyword-only parameters separator (PEP 3102)"><span class="pre">*</span></abbr></span></em>, <em class="sig-param"><span class="n"><span class="pre">counts</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.sample" title="Link to this definition">¶</a></dt>447<dd><p>Return a <em>k</em> length list of unique elements chosen from the population448sequence. Used for random sampling without replacement.</p>449<p>Returns a new list containing elements from the population while leaving the450original population unchanged. The resulting list is in selection order so that451all sub-slices will also be valid random samples. This allows raffle winners452(the sample) to be partitioned into grand prize and second place winners (the453subslices).</p>454<p>Members of the population need not be <a class="reference internal" href="../glossary.html#term-hashable"><span class="xref std std-term">hashable</span></a> or unique. If the population455contains repeats, then each occurrence is a possible selection in the sample.</p>456<p>Repeated elements can be specified one at a time or with the optional457keyword-only <em>counts</em> parameter. For example, <code class="docutils literal notranslate"><span class="pre">sample(['red',</span> <span class="pre">'blue'],</span>458<span class="pre">counts=[4,</span> <span class="pre">2],</span> <span class="pre">k=5)</span></code> is equivalent to <code class="docutils literal notranslate"><span class="pre">sample(['red',</span> <span class="pre">'red',</span> <span class="pre">'red',</span> <span class="pre">'red',</span>459<span class="pre">'blue',</span> <span class="pre">'blue'],</span> <span class="pre">k=5)</span></code>.</p>460<p>To choose a sample from a range of integers, use a <a class="reference internal" href="stdtypes.html#range" title="range"><code class="xref py py-func docutils literal notranslate"><span class="pre">range()</span></code></a> object as an461argument. This is especially fast and space efficient for sampling from a large462population: <code class="docutils literal notranslate"><span class="pre">sample(range(10000000),</span> <span class="pre">k=60)</span></code>.</p>463<p>If the sample size is larger than the population size, a <a class="reference internal" href="exceptions.html#ValueError" title="ValueError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">ValueError</span></code></a>464is raised.</p>465<div class="versionchanged">466<p><span class="versionmodified changed">Changed in version 3.9: </span>Added the <em>counts</em> parameter.</p>467</div>468<div class="versionchanged">469<p><span class="versionmodified changed">Changed in version 3.11: </span>The <em>population</em> must be a sequence. Automatic conversion of sets470to lists is no longer supported.</p>471</div>472</dd></dl>473 474</section>475<section id="discrete-distributions">476<h2>Discrete distributions<a class="headerlink" href="#discrete-distributions" title="Link to this heading">¶</a></h2>477<p>The following function generates a discrete distribution.</p>478<dl class="py function">479<dt class="sig sig-object py" id="random.binomialvariate">480<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">binomialvariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.5</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.binomialvariate" title="Link to this definition">¶</a></dt>481<dd><p><a class="reference external" href="https://mathworld.wolfram.com/BinomialDistribution.html">Binomial distribution</a>.482Return the number of successes for <em>n</em> independent trials with the483probability of success in each trial being <em>p</em>:</p>484<p>Mathematically equivalent to:</p>485<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span><span class="p">(</span><span class="n">random</span><span class="p">()</span> <span class="o"><</span> <span class="n">p</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>486</pre></div>487</div>488<p>The number of trials <em>n</em> should be a non-negative integer.489The probability of success <em>p</em> should be between <code class="docutils literal notranslate"><span class="pre">0.0</span> <span class="pre"><=</span> <span class="pre">p</span> <span class="pre"><=</span> <span class="pre">1.0</span></code>.490The result is an integer in the range <code class="docutils literal notranslate"><span class="pre">0</span> <span class="pre"><=</span> <span class="pre">X</span> <span class="pre"><=</span> <span class="pre">n</span></code>.</p>491<div class="versionadded">492<p><span class="versionmodified added">Added in version 3.12.</span></p>493</div>494</dd></dl>495 496</section>497<section id="real-valued-distributions">498<span id="id1"></span><h2>Real-valued distributions<a class="headerlink" href="#real-valued-distributions" title="Link to this heading">¶</a></h2>499<p>The following functions generate specific real-valued distributions. Function500parameters are named after the corresponding variables in the distribution’s501equation, as used in common mathematical practice; most of these equations can502be found in any statistics text.</p>503<dl class="py function">504<dt class="sig sig-object py" id="random.random">505<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">random</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.random" title="Link to this definition">¶</a></dt>506<dd><p>Return the next random floating-point number in the range <code class="docutils literal notranslate"><span class="pre">0.0</span> <span class="pre"><=</span> <span class="pre">X</span> <span class="pre"><</span> <span class="pre">1.0</span></code></p>507</dd></dl>508 509<dl class="py function">510<dt class="sig sig-object py" id="random.uniform">511<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">uniform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.uniform" title="Link to this definition">¶</a></dt>512<dd><p>Return a random floating-point number <em>N</em> such that <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">b</span></code> for513<code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre"><=</span> <span class="pre">b</span></code> and <code class="docutils literal notranslate"><span class="pre">b</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">a</span></code> for <code class="docutils literal notranslate"><span class="pre">b</span> <span class="pre"><</span> <span class="pre">a</span></code>.</p>514<p>The end-point value <code class="docutils literal notranslate"><span class="pre">b</span></code> may or may not be included in the range515depending on floating-point rounding in the expression516<code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">(b-a)</span> <span class="pre">*</span> <span class="pre">random()</span></code>.</p>517</dd></dl>518 519<dl class="py function">520<dt class="sig sig-object py" id="random.triangular">521<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">triangular</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">low</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">high</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.triangular" title="Link to this definition">¶</a></dt>522<dd><p>Return a random floating-point number <em>N</em> such that <code class="docutils literal notranslate"><span class="pre">low</span> <span class="pre"><=</span> <span class="pre">N</span> <span class="pre"><=</span> <span class="pre">high</span></code> and523with the specified <em>mode</em> between those bounds. The <em>low</em> and <em>high</em> bounds524default to zero and one. The <em>mode</em> argument defaults to the midpoint525between the bounds, giving a symmetric distribution.</p>526</dd></dl>527 528<dl class="py function">529<dt class="sig sig-object py" id="random.betavariate">530<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">betavariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.betavariate" title="Link to this definition">¶</a></dt>531<dd><p>Beta distribution. Conditions on the parameters are <code class="docutils literal notranslate"><span class="pre">alpha</span> <span class="pre">></span> <span class="pre">0</span></code> and532<code class="docutils literal notranslate"><span class="pre">beta</span> <span class="pre">></span> <span class="pre">0</span></code>. Returned values range between 0 and 1.</p>533</dd></dl>534 535<dl class="py function">536<dt class="sig sig-object py" id="random.expovariate">537<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">expovariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lambd</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.expovariate" title="Link to this definition">¶</a></dt>538<dd><p>Exponential distribution. <em>lambd</em> is 1.0 divided by the desired539mean. It should be nonzero. (The parameter would be called540“lambda”, but that is a reserved word in Python.) Returned values541range from 0 to positive infinity if <em>lambd</em> is positive, and from542negative infinity to 0 if <em>lambd</em> is negative.</p>543<div class="versionchanged">544<p><span class="versionmodified changed">Changed in version 3.12: </span>Added the default value for <code class="docutils literal notranslate"><span class="pre">lambd</span></code>.</p>545</div>546</dd></dl>547 548<dl class="py function">549<dt class="sig sig-object py" id="random.gammavariate">550<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">gammavariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.gammavariate" title="Link to this definition">¶</a></dt>551<dd><p>Gamma distribution. (<em>Not</em> the gamma function!) The shape and552scale parameters, <em>alpha</em> and <em>beta</em>, must have positive values.553(Calling conventions vary and some sources define ‘beta’554as the inverse of the scale).</p>555<p>The probability distribution function is:</p>556<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span> <span class="n">x</span> <span class="o">**</span> <span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">x</span> <span class="o">/</span> <span class="n">beta</span><span class="p">)</span>557<span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">=</span> <span class="o">--------------------------------------</span>558 <span class="n">math</span><span class="o">.</span><span class="n">gamma</span><span class="p">(</span><span class="n">alpha</span><span class="p">)</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">**</span> <span class="n">alpha</span>559</pre></div>560</div>561</dd></dl>562 563<dl class="py function">564<dt class="sig sig-object py" id="random.gauss">565<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">gauss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.gauss" title="Link to this definition">¶</a></dt>566<dd><p>Normal distribution, also called the Gaussian distribution.567<em>mu</em> is the mean,568and <em>sigma</em> is the standard deviation. This is slightly faster than569the <a class="reference internal" href="#random.normalvariate" title="random.normalvariate"><code class="xref py py-func docutils literal notranslate"><span class="pre">normalvariate()</span></code></a> function defined below.</p>570<p>Multithreading note: When two threads call this function571simultaneously, it is possible that they will receive the572same return value. This can be avoided in three ways.5731) Have each thread use a different instance of the random574number generator. 2) Put locks around all calls. 3) Use the575slower, but thread-safe <a class="reference internal" href="#random.normalvariate" title="random.normalvariate"><code class="xref py py-func docutils literal notranslate"><span class="pre">normalvariate()</span></code></a> function instead.</p>576<div class="versionchanged">577<p><span class="versionmodified changed">Changed in version 3.11: </span><em>mu</em> and <em>sigma</em> now have default arguments.</p>578</div>579</dd></dl>580 581<dl class="py function">582<dt class="sig sig-object py" id="random.lognormvariate">583<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">lognormvariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.lognormvariate" title="Link to this definition">¶</a></dt>584<dd><p>Log normal distribution. If you take the natural logarithm of this585distribution, you’ll get a normal distribution with mean <em>mu</em> and standard586deviation <em>sigma</em>. <em>mu</em> can have any value, and <em>sigma</em> must be greater than587zero.</p>588</dd></dl>589 590<dl class="py function">591<dt class="sig sig-object py" id="random.normalvariate">592<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">normalvariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.normalvariate" title="Link to this definition">¶</a></dt>593<dd><p>Normal distribution. <em>mu</em> is the mean, and <em>sigma</em> is the standard deviation.</p>594<div class="versionchanged">595<p><span class="versionmodified changed">Changed in version 3.11: </span><em>mu</em> and <em>sigma</em> now have default arguments.</p>596</div>597</dd></dl>598 599<dl class="py function">600<dt class="sig sig-object py" id="random.vonmisesvariate">601<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">vonmisesvariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kappa</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.vonmisesvariate" title="Link to this definition">¶</a></dt>602<dd><p><em>mu</em> is the mean angle, expressed in radians between 0 and 2*<em>pi</em>, and <em>kappa</em>603is the concentration parameter, which must be greater than or equal to zero. If604<em>kappa</em> is equal to zero, this distribution reduces to a uniform random angle605over the range 0 to 2*<em>pi</em>.</p>606</dd></dl>607 608<dl class="py function">609<dt class="sig sig-object py" id="random.paretovariate">610<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">paretovariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.paretovariate" title="Link to this definition">¶</a></dt>611<dd><p>Pareto distribution. <em>alpha</em> is the shape parameter.</p>612</dd></dl>613 614<dl class="py function">615<dt class="sig sig-object py" id="random.weibullvariate">616<span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">weibullvariate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">alpha</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.weibullvariate" title="Link to this definition">¶</a></dt>617<dd><p>Weibull distribution. <em>alpha</em> is the scale parameter and <em>beta</em> is the shape618parameter.</p>619</dd></dl>620 621</section>622<section id="alternative-generator">623<h2>Alternative Generator<a class="headerlink" href="#alternative-generator" title="Link to this heading">¶</a></h2>624<dl class="py class">625<dt class="sig sig-object py" id="random.Random">626<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">Random</span></span><span class="sig-paren">(</span><span class="optional">[</span><em class="sig-param"><span class="n"><span class="pre">seed</span></span></em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.Random" title="Link to this definition">¶</a></dt>627<dd><p>Class that implements the default pseudo-random number generator used by the628<code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> module.</p>629<div class="versionchanged">630<p><span class="versionmodified changed">Changed in version 3.11: </span>Formerly the <em>seed</em> could be any hashable object. Now it is limited to:631<code class="docutils literal notranslate"><span class="pre">None</span></code>, <a class="reference internal" href="functions.html#int" title="int"><code class="xref py py-class docutils literal notranslate"><span class="pre">int</span></code></a>, <a class="reference internal" href="functions.html#float" title="float"><code class="xref py py-class docutils literal notranslate"><span class="pre">float</span></code></a>, <a class="reference internal" href="stdtypes.html#str" title="str"><code class="xref py py-class docutils literal notranslate"><span class="pre">str</span></code></a>,632<a class="reference internal" href="stdtypes.html#bytes" title="bytes"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytes</span></code></a>, or <a class="reference internal" href="stdtypes.html#bytearray" title="bytearray"><code class="xref py py-class docutils literal notranslate"><span class="pre">bytearray</span></code></a>.</p>633</div>634<p>Subclasses of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> should override the following methods if they635wish to make use of a different basic generator:</p>636<dl class="py method">637<dt class="sig sig-object py" id="random.Random.seed">638<span class="sig-name descname"><span class="pre">seed</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">version</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.Random.seed" title="Link to this definition">¶</a></dt>639<dd><p>Override this method in subclasses to customise the <a class="reference internal" href="#random.seed" title="random.seed"><code class="xref py py-meth docutils literal notranslate"><span class="pre">seed()</span></code></a>640behaviour of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> instances.</p>641</dd></dl>642 643<dl class="py method">644<dt class="sig sig-object py" id="random.Random.getstate">645<span class="sig-name descname"><span class="pre">getstate</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.Random.getstate" title="Link to this definition">¶</a></dt>646<dd><p>Override this method in subclasses to customise the <a class="reference internal" href="#random.getstate" title="random.getstate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">getstate()</span></code></a>647behaviour of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> instances.</p>648</dd></dl>649 650<dl class="py method">651<dt class="sig sig-object py" id="random.Random.setstate">652<span class="sig-name descname"><span class="pre">setstate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">state</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.Random.setstate" title="Link to this definition">¶</a></dt>653<dd><p>Override this method in subclasses to customise the <a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">setstate()</span></code></a>654behaviour of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> instances.</p>655</dd></dl>656 657<dl class="py method">658<dt class="sig sig-object py" id="random.Random.random">659<span class="sig-name descname"><span class="pre">random</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.Random.random" title="Link to this definition">¶</a></dt>660<dd><p>Override this method in subclasses to customise the <a class="reference internal" href="#random.random" title="random.random"><code class="xref py py-meth docutils literal notranslate"><span class="pre">random()</span></code></a>661behaviour of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> instances.</p>662</dd></dl>663 664<p>Optionally, a custom generator subclass can also supply the following method:</p>665<dl class="py method">666<dt class="sig sig-object py" id="random.Random.getrandbits">667<span class="sig-name descname"><span class="pre">getrandbits</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">k</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.Random.getrandbits" title="Link to this definition">¶</a></dt>668<dd><p>Override this method in subclasses to customise the669<a class="reference internal" href="#random.getrandbits" title="random.getrandbits"><code class="xref py py-meth docutils literal notranslate"><span class="pre">getrandbits()</span></code></a> behaviour of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> instances.</p>670</dd></dl>671 672<dl class="py method">673<dt class="sig sig-object py" id="random.Random.randbytes">674<span class="sig-name descname"><span class="pre">randbytes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#random.Random.randbytes" title="Link to this definition">¶</a></dt>675<dd><p>Override this method in subclasses to customise the676<a class="reference internal" href="#random.randbytes" title="random.randbytes"><code class="xref py py-meth docutils literal notranslate"><span class="pre">randbytes()</span></code></a> behaviour of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> instances.</p>677</dd></dl>678 679</dd></dl>680 681<dl class="py class">682<dt class="sig sig-object py" id="random.SystemRandom">683<em class="property"><span class="k"><span class="pre">class</span></span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">random.</span></span><span class="sig-name descname"><span class="pre">SystemRandom</span></span><span class="sig-paren">(</span><span class="optional">[</span><em class="sig-param"><span class="n"><span class="pre">seed</span></span></em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.SystemRandom" title="Link to this definition">¶</a></dt>684<dd><p>Class that uses the <a class="reference internal" href="os.html#os.urandom" title="os.urandom"><code class="xref py py-func docutils literal notranslate"><span class="pre">os.urandom()</span></code></a> function for generating random numbers685from sources provided by the operating system. Not available on all systems.686Does not rely on software state, and sequences are not reproducible. Accordingly,687the <a class="reference internal" href="#random.seed" title="random.seed"><code class="xref py py-meth docutils literal notranslate"><span class="pre">seed()</span></code></a> method has no effect and is ignored.688The <a class="reference internal" href="#random.getstate" title="random.getstate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">getstate()</span></code></a> and <a class="reference internal" href="#random.setstate" title="random.setstate"><code class="xref py py-meth docutils literal notranslate"><span class="pre">setstate()</span></code></a> methods raise689<a class="reference internal" href="exceptions.html#NotImplementedError" title="NotImplementedError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">NotImplementedError</span></code></a> if called.</p>690</dd></dl>691 692</section>693<section id="notes-on-reproducibility">694<h2>Notes on Reproducibility<a class="headerlink" href="#notes-on-reproducibility" title="Link to this heading">¶</a></h2>695<p>Sometimes it is useful to be able to reproduce the sequences given by a696pseudo-random number generator. By reusing a seed value, the same sequence should be697reproducible from run to run as long as multiple threads are not running.</p>698<p>Most of the random module’s algorithms and seeding functions are subject to699change across Python versions, but two aspects are guaranteed not to change:</p>700<ul class="simple">701<li><p>If a new seeding method is added, then a backward compatible seeder will be702offered.</p></li>703<li><p>The generator’s <a class="reference internal" href="#random.Random.random" title="random.Random.random"><code class="xref py py-meth docutils literal notranslate"><span class="pre">random()</span></code></a> method will continue to produce the same704sequence when the compatible seeder is given the same seed.</p></li>705</ul>706</section>707<section id="examples">708<span id="random-examples"></span><h2>Examples<a class="headerlink" href="#examples" title="Link to this heading">¶</a></h2>709<p>Basic examples:</p>710<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">random</span><span class="p">()</span> <span class="c1"># Random float: 0.0 <= x < 1.0</span>711<span class="go">0.37444887175646646</span>712 713<span class="gp">>>> </span><span class="n">uniform</span><span class="p">(</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">)</span> <span class="c1"># Random float: 2.5 <= x <= 10.0</span>714<span class="go">3.1800146073117523</span>715 716<span class="gp">>>> </span><span class="n">expovariate</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">5</span><span class="p">)</span> <span class="c1"># Interval between arrivals averaging 5 seconds</span>717<span class="go">5.148957571865031</span>718 719<span class="gp">>>> </span><span class="n">randrange</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span> <span class="c1"># Integer from 0 to 9 inclusive</span>720<span class="go">7</span>721 722<span class="gp">>>> </span><span class="n">randrange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">101</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># Even integer from 0 to 100 inclusive</span>723<span class="go">26</span>724 725<span class="gp">>>> </span><span class="n">choice</span><span class="p">([</span><span class="s1">'win'</span><span class="p">,</span> <span class="s1">'lose'</span><span class="p">,</span> <span class="s1">'draw'</span><span class="p">])</span> <span class="c1"># Single random element from a sequence</span>726<span class="go">'draw'</span>727 728<span class="gp">>>> </span><span class="n">deck</span> <span class="o">=</span> <span class="s1">'ace two three four'</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>729<span class="gp">>>> </span><span class="n">shuffle</span><span class="p">(</span><span class="n">deck</span><span class="p">)</span> <span class="c1"># Shuffle a list</span>730<span class="gp">>>> </span><span class="n">deck</span>731<span class="go">['four', 'two', 'ace', 'three']</span>732 733<span class="gp">>>> </span><span class="n">sample</span><span class="p">([</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">40</span><span class="p">,</span> <span class="mi">50</span><span class="p">],</span> <span class="n">k</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span> <span class="c1"># Four samples without replacement</span>734<span class="go">[40, 10, 50, 30]</span>735</pre></div>736</div>737<p>Simulations:</p>738<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># Six roulette wheel spins (weighted sampling with replacement)</span>739<span class="gp">>>> </span><span class="n">choices</span><span class="p">([</span><span class="s1">'red'</span><span class="p">,</span> <span class="s1">'black'</span><span class="p">,</span> <span class="s1">'green'</span><span class="p">],</span> <span class="p">[</span><span class="mi">18</span><span class="p">,</span> <span class="mi">18</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">k</span><span class="o">=</span><span class="mi">6</span><span class="p">)</span>740<span class="go">['red', 'green', 'black', 'black', 'red', 'black']</span>741 742<span class="gp">>>> </span><span class="c1"># Deal 20 cards without replacement from a deck</span>743<span class="gp">>>> </span><span class="c1"># of 52 playing cards, and determine the proportion of cards</span>744<span class="gp">>>> </span><span class="c1"># with a ten-value: ten, jack, queen, or king.</span>745<span class="gp">>>> </span><span class="n">deal</span> <span class="o">=</span> <span class="n">sample</span><span class="p">([</span><span class="s1">'tens'</span><span class="p">,</span> <span class="s1">'low cards'</span><span class="p">],</span> <span class="n">counts</span><span class="o">=</span><span class="p">[</span><span class="mi">16</span><span class="p">,</span> <span class="mi">36</span><span class="p">],</span> <span class="n">k</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>746<span class="gp">>>> </span><span class="n">deal</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="s1">'tens'</span><span class="p">)</span> <span class="o">/</span> <span class="mi">20</span>747<span class="go">0.15</span>748 749<span class="gp">>>> </span><span class="c1"># Estimate the probability of getting 5 or more heads from 7 spins</span>750<span class="gp">>>> </span><span class="c1"># of a biased coin that settles on heads 60% of the time.</span>751<span class="gp">>>> </span><span class="nb">sum</span><span class="p">(</span><span class="n">binomialvariate</span><span class="p">(</span><span class="n">n</span><span class="o">=</span><span class="mi">7</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="mf">0.6</span><span class="p">)</span> <span class="o">>=</span> <span class="mi">5</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10_000</span><span class="p">))</span> <span class="o">/</span> <span class="mi">10_000</span>752<span class="go">0.4169</span>753 754<span class="gp">>>> </span><span class="c1"># Probability of the median of 5 samples being in middle two quartiles</span>755<span class="gp">>>> </span><span class="k">def</span><span class="w"> </span><span class="nf">trial</span><span class="p">():</span>756<span class="gp">... </span> <span class="k">return</span> <span class="mi">2_500</span> <span class="o"><=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">choices</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">10_000</span><span class="p">),</span> <span class="n">k</span><span class="o">=</span><span class="mi">5</span><span class="p">))[</span><span class="mi">2</span><span class="p">]</span> <span class="o"><</span> <span class="mi">7_500</span>757<span class="gp">...</span>758<span class="gp">>>> </span><span class="nb">sum</span><span class="p">(</span><span class="n">trial</span><span class="p">()</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10_000</span><span class="p">))</span> <span class="o">/</span> <span class="mi">10_000</span>759<span class="go">0.7958</span>760</pre></div>761</div>762<p>Example of <a class="reference external" href="https://en.wikipedia.org/wiki/Bootstrapping_(statistics)">statistical bootstrapping</a> using resampling763with replacement to estimate a confidence interval for the mean of a sample:</p>764<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># https://www.thoughtco.com/example-of-bootstrapping-3126155</span>765<span class="kn">from</span><span class="w"> </span><span class="nn">statistics</span><span class="w"> </span><span class="kn">import</span> <span class="n">fmean</span> <span class="k">as</span> <span class="n">mean</span>766<span class="kn">from</span><span class="w"> </span><span class="nn">random</span><span class="w"> </span><span class="kn">import</span> <span class="n">choices</span>767 768<span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="mi">41</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">29</span><span class="p">,</span> <span class="mi">37</span><span class="p">,</span> <span class="mi">81</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">73</span><span class="p">,</span> <span class="mi">63</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="mi">35</span><span class="p">,</span> <span class="mi">68</span><span class="p">,</span> <span class="mi">22</span><span class="p">,</span> <span class="mi">60</span><span class="p">,</span> <span class="mi">31</span><span class="p">,</span> <span class="mi">95</span><span class="p">]</span>769<span class="n">means</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">mean</span><span class="p">(</span><span class="n">choices</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)))</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">))</span>770<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The sample mean of </span><span class="si">{</span><span class="n">mean</span><span class="p">(</span><span class="n">data</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> has a 90% confidence '</span>771 <span class="sa">f</span><span class="s1">'interval from </span><span class="si">{</span><span class="n">means</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> to </span><span class="si">{</span><span class="n">means</span><span class="p">[</span><span class="mi">94</span><span class="p">]</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>772</pre></div>773</div>774<p>Example of a <a class="reference external" href="https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests">resampling permutation test</a>775to determine the statistical significance or <a class="reference external" href="https://en.wikipedia.org/wiki/P-value">p-value</a> of an observed difference776between the effects of a drug versus a placebo:</p>777<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson</span>778<span class="kn">from</span><span class="w"> </span><span class="nn">statistics</span><span class="w"> </span><span class="kn">import</span> <span class="n">fmean</span> <span class="k">as</span> <span class="n">mean</span>779<span class="kn">from</span><span class="w"> </span><span class="nn">random</span><span class="w"> </span><span class="kn">import</span> <span class="n">shuffle</span>780 781<span class="n">drug</span> <span class="o">=</span> <span class="p">[</span><span class="mi">54</span><span class="p">,</span> <span class="mi">73</span><span class="p">,</span> <span class="mi">53</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">73</span><span class="p">,</span> <span class="mi">68</span><span class="p">,</span> <span class="mi">52</span><span class="p">,</span> <span class="mi">65</span><span class="p">,</span> <span class="mi">65</span><span class="p">]</span>782<span class="n">placebo</span> <span class="o">=</span> <span class="p">[</span><span class="mi">54</span><span class="p">,</span> <span class="mi">51</span><span class="p">,</span> <span class="mi">58</span><span class="p">,</span> <span class="mi">44</span><span class="p">,</span> <span class="mi">55</span><span class="p">,</span> <span class="mi">52</span><span class="p">,</span> <span class="mi">42</span><span class="p">,</span> <span class="mi">47</span><span class="p">,</span> <span class="mi">58</span><span class="p">,</span> <span class="mi">46</span><span class="p">]</span>783<span class="n">observed_diff</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">drug</span><span class="p">)</span> <span class="o">-</span> <span class="n">mean</span><span class="p">(</span><span class="n">placebo</span><span class="p">)</span>784 785<span class="n">n</span> <span class="o">=</span> <span class="mi">10_000</span>786<span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>787<span class="n">combined</span> <span class="o">=</span> <span class="n">drug</span> <span class="o">+</span> <span class="n">placebo</span>788<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>789 <span class="n">shuffle</span><span class="p">(</span><span class="n">combined</span><span class="p">)</span>790 <span class="n">new_diff</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">combined</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="n">drug</span><span class="p">)])</span> <span class="o">-</span> <span class="n">mean</span><span class="p">(</span><span class="n">combined</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">drug</span><span class="p">):])</span>791 <span class="n">count</span> <span class="o">+=</span> <span class="p">(</span><span class="n">new_diff</span> <span class="o">>=</span> <span class="n">observed_diff</span><span class="p">)</span>792 793<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s1"> label reshufflings produced only </span><span class="si">{</span><span class="n">count</span><span class="si">}</span><span class="s1"> instances with a difference'</span><span class="p">)</span>794<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'at least as extreme as the observed difference of </span><span class="si">{</span><span class="n">observed_diff</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">.'</span><span class="p">)</span>795<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'The one-sided p-value of </span><span class="si">{</span><span class="n">count</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">n</span><span class="si">:</span><span class="s1">.4f</span><span class="si">}</span><span class="s1"> leads us to reject the null'</span><span class="p">)</span>796<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'hypothesis that there is no difference between the drug and the placebo.'</span><span class="p">)</span>797</pre></div>798</div>799<p>Simulation of arrival times and service deliveries for a multiserver queue:</p>800<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">heapq</span><span class="w"> </span><span class="kn">import</span> <span class="n">heapify</span><span class="p">,</span> <span class="n">heapreplace</span>801<span class="kn">from</span><span class="w"> </span><span class="nn">random</span><span class="w"> </span><span class="kn">import</span> <span class="n">expovariate</span><span class="p">,</span> <span class="n">gauss</span>802<span class="kn">from</span><span class="w"> </span><span class="nn">statistics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean</span><span class="p">,</span> <span class="n">quantiles</span>803 804<span class="n">average_arrival_interval</span> <span class="o">=</span> <span class="mf">5.6</span>805<span class="n">average_service_time</span> <span class="o">=</span> <span class="mf">15.0</span>806<span class="n">stdev_service_time</span> <span class="o">=</span> <span class="mf">3.5</span>807<span class="n">num_servers</span> <span class="o">=</span> <span class="mi">3</span>808 809<span class="n">waits</span> <span class="o">=</span> <span class="p">[]</span>810<span class="n">arrival_time</span> <span class="o">=</span> <span class="mf">0.0</span>811<span class="n">servers</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">]</span> <span class="o">*</span> <span class="n">num_servers</span> <span class="c1"># time when each server becomes available</span>812<span class="n">heapify</span><span class="p">(</span><span class="n">servers</span><span class="p">)</span>813<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1_000_000</span><span class="p">):</span>814 <span class="n">arrival_time</span> <span class="o">+=</span> <span class="n">expovariate</span><span class="p">(</span><span class="mf">1.0</span> <span class="o">/</span> <span class="n">average_arrival_interval</span><span class="p">)</span>815 <span class="n">next_server_available</span> <span class="o">=</span> <span class="n">servers</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>816 <span class="n">wait</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">next_server_available</span> <span class="o">-</span> <span class="n">arrival_time</span><span class="p">)</span>817 <span class="n">waits</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">wait</span><span class="p">)</span>818 <span class="n">service_duration</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">gauss</span><span class="p">(</span><span class="n">average_service_time</span><span class="p">,</span> <span class="n">stdev_service_time</span><span class="p">))</span>819 <span class="n">service_completed</span> <span class="o">=</span> <span class="n">arrival_time</span> <span class="o">+</span> <span class="n">wait</span> <span class="o">+</span> <span class="n">service_duration</span>820 <span class="n">heapreplace</span><span class="p">(</span><span class="n">servers</span><span class="p">,</span> <span class="n">service_completed</span><span class="p">)</span>821 822<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Mean wait: </span><span class="si">{</span><span class="n">mean</span><span class="p">(</span><span class="n">waits</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1"> Max wait: </span><span class="si">{</span><span class="nb">max</span><span class="p">(</span><span class="n">waits</span><span class="p">)</span><span class="si">:</span><span class="s1">.1f</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>823<span class="nb">print</span><span class="p">(</span><span class="s1">'Quartiles:'</span><span class="p">,</span> <span class="p">[</span><span class="nb">round</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">q</span> <span class="ow">in</span> <span class="n">quantiles</span><span class="p">(</span><span class="n">waits</span><span class="p">)])</span>824</pre></div>825</div>826<div class="admonition seealso">827<p class="admonition-title">See also</p>828<p><a class="reference external" href="https://www.youtube.com/watch?v=Iq9DzN6mvYA">Statistics for Hackers</a>829a video tutorial by830<a class="reference external" href="https://us.pycon.org/2016/speaker/profile/295/">Jake Vanderplas</a>831on statistical analysis using just a few fundamental concepts832including simulation, sampling, shuffling, and cross-validation.</p>833<p><a class="reference external" href="https://nbviewer.org/url/norvig.com/ipython/Economics.ipynb">Economics Simulation</a>834a simulation of a marketplace by835<a class="reference external" href="https://norvig.com/bio.html">Peter Norvig</a> that shows effective836use of many of the tools and distributions provided by this module837(gauss, uniform, sample, betavariate, choice, triangular, and randrange).</p>838<p><a class="reference external" href="https://nbviewer.org/url/norvig.com/ipython/Probability.ipynb">A Concrete Introduction to Probability (using Python)</a>839a tutorial by <a class="reference external" href="https://norvig.com/bio.html">Peter Norvig</a> covering840the basics of probability theory, how to write simulations, and841how to perform data analysis using Python.</p>842</div>843</section>844<section id="recipes">845<h2>Recipes<a class="headerlink" href="#recipes" title="Link to this heading">¶</a></h2>846<p>These recipes show how to efficiently make random selections847from the combinatoric iterators in the <a class="reference internal" href="itertools.html#module-itertools" title="itertools: Functions creating iterators for efficient looping."><code class="xref py py-mod docutils literal notranslate"><span class="pre">itertools</span></code></a> module848or the <a class="extlink-pypi reference external" href="https://pypi.org/project/more-itertools/">more-itertools</a> project:</p>849<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">random</span>850 851<span class="k">def</span><span class="w"> </span><span class="nf">random_product</span><span class="p">(</span><span class="o">*</span><span class="n">iterables</span><span class="p">,</span> <span class="n">repeat</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>852 <span class="s2">"Random selection from itertools.product(*iterables, repeat=repeat)"</span>853 <span class="n">pools</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">tuple</span><span class="p">,</span> <span class="n">iterables</span><span class="p">))</span> <span class="o">*</span> <span class="n">repeat</span>854 <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">,</span> <span class="n">pools</span><span class="p">))</span>855 856<span class="k">def</span><span class="w"> </span><span class="nf">random_permutation</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>857 <span class="s2">"Random selection from itertools.permutations(iterable, r)"</span>858 <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>859 <span class="n">r</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span> <span class="k">if</span> <span class="n">r</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">else</span> <span class="n">r</span>860 <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="n">pool</span><span class="p">,</span> <span class="n">r</span><span class="p">))</span>861 862<span class="k">def</span><span class="w"> </span><span class="nf">random_combination</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>863 <span class="s2">"Random selection from itertools.combinations(iterable, r)"</span>864 <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>865 <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>866 <span class="n">indices</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">r</span><span class="p">))</span>867 <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>868 869<span class="k">def</span><span class="w"> </span><span class="nf">random_combination_with_replacement</span><span class="p">(</span><span class="n">iterable</span><span class="p">,</span> <span class="n">r</span><span class="p">):</span>870 <span class="s2">"Choose r elements with replacement. Order the result to match the iterable."</span>871 <span class="c1"># Result will be in set(itertools.combinations_with_replacement(iterable, r)).</span>872 <span class="n">pool</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>873 <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">pool</span><span class="p">)</span>874 <span class="n">indices</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">choices</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">),</span> <span class="n">k</span><span class="o">=</span><span class="n">r</span><span class="p">))</span>875 <span class="k">return</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">pool</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">indices</span><span class="p">)</span>876 877<span class="k">def</span><span class="w"> </span><span class="nf">random_derangement</span><span class="p">(</span><span class="n">iterable</span><span class="p">):</span>878 <span class="s2">"Choose a permutation where no element stays in its original position."</span>879 <span class="n">seq</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">iterable</span><span class="p">)</span>880 <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">seq</span><span class="p">)</span> <span class="o"><</span> <span class="mi">2</span><span class="p">:</span>881 <span class="k">if</span> <span class="ow">not</span> <span class="n">seq</span><span class="p">:</span>882 <span class="k">return</span> <span class="p">()</span>883 <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s1">'No derangments to choose from'</span><span class="p">)</span>884 <span class="n">perm</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">seq</span><span class="p">)))</span>885 <span class="n">start</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">perm</span><span class="p">)</span>886 <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>887 <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">perm</span><span class="p">)</span>888 <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">p</span> <span class="o">!=</span> <span class="n">q</span> <span class="k">for</span> <span class="n">p</span><span class="p">,</span> <span class="n">q</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">perm</span><span class="p">)):</span>889 <span class="k">return</span> <span class="nb">tuple</span><span class="p">([</span><span class="n">seq</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">perm</span><span class="p">])</span>890</pre></div>891</div>892<p>The default <a class="reference internal" href="#random.random" title="random.random"><code class="xref py py-func docutils literal notranslate"><span class="pre">random()</span></code></a> returns multiples of 2⁻⁵³ in the range893<em>0.0 ≤ x < 1.0</em>. All such numbers are evenly spaced and are exactly894representable as Python floats. However, many other representable895floats in that interval are not possible selections. For example,896<code class="docutils literal notranslate"><span class="pre">0.05954861408025609</span></code> isn’t an integer multiple of 2⁻⁵³.</p>897<p>The following recipe takes a different approach. All floats in the898interval are possible selections. The mantissa comes from a uniform899distribution of integers in the range <em>2⁵² ≤ mantissa < 2⁵³</em>. The900exponent comes from a geometric distribution where exponents smaller901than <em>-53</em> occur half as often as the next larger exponent.</p>902<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">random</span><span class="w"> </span><span class="kn">import</span> <span class="n">Random</span>903<span class="kn">from</span><span class="w"> </span><span class="nn">math</span><span class="w"> </span><span class="kn">import</span> <span class="n">ldexp</span>904 905<span class="k">class</span><span class="w"> </span><span class="nc">FullRandom</span><span class="p">(</span><span class="n">Random</span><span class="p">):</span>906 907 <span class="k">def</span><span class="w"> </span><span class="nf">random</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>908 <span class="n">mantissa</span> <span class="o">=</span> <span class="mh">0x10_0000_0000_0000</span> <span class="o">|</span> <span class="bp">self</span><span class="o">.</span><span class="n">getrandbits</span><span class="p">(</span><span class="mi">52</span><span class="p">)</span>909 <span class="n">exponent</span> <span class="o">=</span> <span class="o">-</span><span class="mi">53</span>910 <span class="n">x</span> <span class="o">=</span> <span class="mi">0</span>911 <span class="k">while</span> <span class="ow">not</span> <span class="n">x</span><span class="p">:</span>912 <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">getrandbits</span><span class="p">(</span><span class="mi">32</span><span class="p">)</span>913 <span class="n">exponent</span> <span class="o">+=</span> <span class="n">x</span><span class="o">.</span><span class="n">bit_length</span><span class="p">()</span> <span class="o">-</span> <span class="mi">32</span>914 <span class="k">return</span> <span class="n">ldexp</span><span class="p">(</span><span class="n">mantissa</span><span class="p">,</span> <span class="n">exponent</span><span class="p">)</span>915</pre></div>916</div>917<p>All <a class="reference internal" href="#real-valued-distributions"><span class="std std-ref">real valued distributions</span></a>918in the class will use the new method:</p>919<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">fr</span> <span class="o">=</span> <span class="n">FullRandom</span><span class="p">()</span>920<span class="gp">>>> </span><span class="n">fr</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>921<span class="go">0.05954861408025609</span>922<span class="gp">>>> </span><span class="n">fr</span><span class="o">.</span><span class="n">expovariate</span><span class="p">(</span><span class="mf">0.25</span><span class="p">)</span>923<span class="go">8.87925541791544</span>924</pre></div>925</div>926<p>The recipe is conceptually equivalent to an algorithm that chooses from927all the multiples of 2⁻¹⁰⁷⁴ in the range <em>0.0 ≤ x < 1.0</em>. All such928numbers are evenly spaced, but most have to be rounded down to the929nearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallest930positive unnormalized float and is equal to <code class="docutils literal notranslate"><span class="pre">math.ulp(0.0)</span></code>.)</p>931<div class="admonition seealso">932<p class="admonition-title">See also</p>933<p><a class="reference external" href="https://allendowney.com/research/rand/downey07randfloat.pdf">Generating Pseudo-random Floating-Point Values</a> a934paper by Allen B. Downey describing ways to generate more935fine-grained floats than normally generated by <a class="reference internal" href="#random.random" title="random.random"><code class="xref py py-func docutils literal notranslate"><span class="pre">random()</span></code></a>.</p>936</div>937</section>938<section id="command-line-usage">939<span id="random-cli"></span><h2>Command-line usage<a class="headerlink" href="#command-line-usage" title="Link to this heading">¶</a></h2>940<div class="versionadded">941<p><span class="versionmodified added">Added in version 3.13.</span></p>942</div>943<p>The <code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> module can be executed from the command line.</p>944<div class="highlight-sh notranslate"><div class="highlight"><pre><span></span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span><span class="o">[</span>-h<span class="o">]</span><span class="w"> </span><span class="o">[</span>-c<span class="w"> </span>CHOICE<span class="w"> </span><span class="o">[</span>CHOICE<span class="w"> </span>...<span class="o">]</span><span class="w"> </span><span class="p">|</span><span class="w"> </span>-i<span class="w"> </span>N<span class="w"> </span><span class="p">|</span><span class="w"> </span>-f<span class="w"> </span>N<span class="o">]</span><span class="w"> </span><span class="o">[</span>input<span class="w"> </span>...<span class="o">]</span>945</pre></div>946</div>947<p>The following options are accepted:</p>948<dl class="std option">949<dt class="sig sig-object std" id="cmdoption-random-h">950<span id="cmdoption-random-help"></span><span class="sig-name descname"><span class="pre">-h</span></span><span class="sig-prename descclassname"></span><span class="sig-prename descclassname"><span class="pre">,</span> </span><span class="sig-name descname"><span class="pre">--help</span></span><span class="sig-prename descclassname"></span><a class="headerlink" href="#cmdoption-random-h" title="Link to this definition">¶</a></dt>951<dd><p>Show the help message and exit.</p>952</dd></dl>953 954<dl class="std option">955<dt class="sig sig-object std" id="cmdoption-random-c">956<span class="sig-name descname"><span class="pre">-c</span></span><span class="sig-prename descclassname"> <span class="pre">CHOICE</span> <span class="pre">[CHOICE</span> <span class="pre">...]</span></span><a class="headerlink" href="#cmdoption-random-c" title="Link to this definition">¶</a></dt>957<dt class="sig sig-object std" id="cmdoption-random-choice">958<span class="sig-name descname"><span class="pre">--choice</span></span><span class="sig-prename descclassname"> <span class="pre">CHOICE</span> <span class="pre">[CHOICE</span> <span class="pre">...]</span></span><a class="headerlink" href="#cmdoption-random-choice" title="Link to this definition">¶</a></dt>959<dd><p>Print a random choice, using <a class="reference internal" href="#random.choice" title="random.choice"><code class="xref py py-meth docutils literal notranslate"><span class="pre">choice()</span></code></a>.</p>960</dd></dl>961 962<dl class="std option">963<dt class="sig sig-object std" id="cmdoption-random-i">964<span class="sig-name descname"><span class="pre">-i</span></span><span class="sig-prename descclassname"> <span class="pre"><N></span></span><a class="headerlink" href="#cmdoption-random-i" title="Link to this definition">¶</a></dt>965<dt class="sig sig-object std" id="cmdoption-random-integer">966<span class="sig-name descname"><span class="pre">--integer</span></span><span class="sig-prename descclassname"> <span class="pre"><N></span></span><a class="headerlink" href="#cmdoption-random-integer" title="Link to this definition">¶</a></dt>967<dd><p>Print a random integer between 1 and N inclusive, using <a class="reference internal" href="#random.randint" title="random.randint"><code class="xref py py-meth docutils literal notranslate"><span class="pre">randint()</span></code></a>.</p>968</dd></dl>969 970<dl class="std option">971<dt class="sig sig-object std" id="cmdoption-random-f">972<span class="sig-name descname"><span class="pre">-f</span></span><span class="sig-prename descclassname"> <span class="pre"><N></span></span><a class="headerlink" href="#cmdoption-random-f" title="Link to this definition">¶</a></dt>973<dt class="sig sig-object std" id="cmdoption-random-float">974<span class="sig-name descname"><span class="pre">--float</span></span><span class="sig-prename descclassname"> <span class="pre"><N></span></span><a class="headerlink" href="#cmdoption-random-float" title="Link to this definition">¶</a></dt>975<dd><p>Print a random floating-point number between 0 and N inclusive,976using <a class="reference internal" href="#random.uniform" title="random.uniform"><code class="xref py py-meth docutils literal notranslate"><span class="pre">uniform()</span></code></a>.</p>977</dd></dl>978 979<p>If no options are given, the output depends on the input:</p>980<ul class="simple">981<li><p>String or multiple: same as <a class="reference internal" href="#cmdoption-random-choice"><code class="xref std std-option docutils literal notranslate"><span class="pre">--choice</span></code></a>.</p></li>982<li><p>Integer: same as <a class="reference internal" href="#cmdoption-random-integer"><code class="xref std std-option docutils literal notranslate"><span class="pre">--integer</span></code></a>.</p></li>983<li><p>Float: same as <a class="reference internal" href="#cmdoption-random-float"><code class="xref std std-option docutils literal notranslate"><span class="pre">--float</span></code></a>.</p></li>984</ul>985</section>986<section id="command-line-example">987<span id="random-cli-example"></span><h2>Command-line example<a class="headerlink" href="#command-line-example" title="Link to this heading">¶</a></h2>988<p>Here are some examples of the <code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> command-line interface:</p>989<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="gp">$ </span><span class="c1"># Choose one at random</span>990<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span>egg<span class="w"> </span>bacon<span class="w"> </span>sausage<span class="w"> </span>spam<span class="w"> </span><span class="s2">"Lobster Thermidor aux crevettes with a Mornay sauce"</span>991<span class="go">Lobster Thermidor aux crevettes with a Mornay sauce</span>992 993<span class="gp">$ </span><span class="c1"># Random integer</span>994<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span><span class="m">6</span>995<span class="go">6</span>996 997<span class="gp">$ </span><span class="c1"># Random floating-point number</span>998<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span><span class="m">1</span>.8999<span class="go">1.7080016272295635</span>1000 1001<span class="gp">$ </span><span class="c1"># With explicit arguments</span>1002<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span>--choice<span class="w"> </span>egg<span class="w"> </span>bacon<span class="w"> </span>sausage<span class="w"> </span>spam<span class="w"> </span><span class="s2">"Lobster Thermidor aux crevettes with a Mornay sauce"</span>1003<span class="go">egg</span>1004 1005<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span>--integer<span class="w"> </span><span class="m">6</span>1006<span class="go">3</span>1007 1008<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span>--float<span class="w"> </span><span class="m">1</span>.81009<span class="go">1.5666339105010318</span>1010 1011<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span>--integer<span class="w"> </span><span class="m">6</span>1012<span class="go">5</span>1013 1014<span class="gp">$ </span>python<span class="w"> </span>-m<span class="w"> </span>random<span class="w"> </span>--float<span class="w"> </span><span class="m">6</span>1015<span class="go">3.1942323316565915</span>1016</pre></div>1017</div>1018</section>1019</section>1020 1021 1022 <div class="clearer"></div>1023 </div>1024 </div>1025 </div>1026 <div class="sphinxsidebar" role="navigation" aria-label="Main">1027 <div class="sphinxsidebarwrapper">1028 <div>1029 <h3><a href="../contents.html">Table of Contents</a></h3>1030 <ul>1031<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers</a><ul>1032<li><a class="reference internal" href="#bookkeeping-functions">Bookkeeping functions</a></li>1033<li><a class="reference internal" href="#functions-for-bytes">Functions for bytes</a></li>1034<li><a class="reference internal" href="#functions-for-integers">Functions for integers</a></li>1035<li><a class="reference internal" href="#functions-for-sequences">Functions for sequences</a></li>1036<li><a class="reference internal" href="#discrete-distributions">Discrete distributions</a></li>1037<li><a class="reference internal" href="#real-valued-distributions">Real-valued distributions</a></li>1038<li><a class="reference internal" href="#alternative-generator">Alternative Generator</a></li>1039<li><a class="reference internal" href="#notes-on-reproducibility">Notes on Reproducibility</a></li>1040<li><a class="reference internal" href="#examples">Examples</a></li>1041<li><a class="reference internal" href="#recipes">Recipes</a></li>1042<li><a class="reference internal" href="#command-line-usage">Command-line usage</a></li>1043<li><a class="reference internal" href="#command-line-example">Command-line example</a></li>1044</ul>1045</li>1046</ul>1047 1048 </div>1049 <div>1050 <h4>Previous topic</h4>1051 <p class="topless"><a href="fractions.html"1052 title="previous chapter"><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code> — Rational numbers</a></p>1053 </div>1054 <div>1055 <h4>Next topic</h4>1056 <p class="topless"><a href="statistics.html"1057 title="next chapter"><code class="xref py py-mod docutils literal notranslate"><span class="pre">statistics</span></code> — Mathematical statistics functions</a></p>1058 </div>1059 <script>1060 document.addEventListener('DOMContentLoaded', () => {1061 const title = document.querySelector('meta[property="og:title"]').content;1062 const elements = document.querySelectorAll('.improvepage');1063 const pageurl = window.location.href.split('?')[0];1064 elements.forEach(element => {1065 const url = new URL(element.href.split('?')[0].replace("-nojs", ""));1066 url.searchParams.set('pagetitle', title);1067 url.searchParams.set('pageurl', pageurl);1068 url.searchParams.set('pagesource', "library/random.rst");1069 element.href = url.toString();1070 });1071 });1072 </script>1073 <div role="note" aria-label="source link">1074 <h3>This page</h3>1075 <ul class="this-page-menu">1076 <li><a href="../bugs.html">Report a bug</a></li>1077 <li><a class="improvepage" href="../improve-page-nojs.html">Improve this page</a></li>1078 <li>1079 <a href="https://github.com/python/cpython/blob/main/Doc/library/random.rst?plain=1"1080 rel="nofollow">Show source1081 </a>1082 </li>1083 1084 </ul>1085 </div>1086 </div>1087<div id="sidebarbutton" title="Collapse sidebar">1088<span>«</span>1089</div>1090 1091 </div>1092 <div class="clearer"></div>1093 </div> 1094 <div class="related" role="navigation" aria-label="Related">1095 <h3>Navigation</h3>1096 <ul>1097 <li class="right" style="margin-right: 10px">1098 <a href="../genindex.html" title="General Index"1099 >index</a></li>1100 <li class="right" >1101 <a href="../py-modindex.html" title="Python Module Index"1102 >modules</a> |</li>1103 <li class="right" >1104 <a href="statistics.html" title="statistics — Mathematical statistics functions"1105 >next</a> |</li>1106 <li class="right" >1107 <a href="fractions.html" title="fractions — Rational numbers"1108 >previous</a> |</li>1109 1110 <li><img src="../_static/py.svg" alt="Python logo" style="vertical-align: middle; margin-top: -1px"></li>1111 <li><a href="https://www.python.org/">Python</a> »</li>1112 <li class="switchers">1113 <div class="language_switcher_placeholder"></div>1114 <div class="version_switcher_placeholder"></div>1115 </li>1116 <li>1117 1118 </li>1119 <li id="cpython-language-and-version">1120 <a href="../index.html">3.15.0a6 Documentation</a> »1121 </li>1122 1123 <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li>1124 <li class="nav-item nav-item-2"><a href="numeric.html" >Numeric and Mathematical Modules</a> »</li>1125 <li class="nav-item nav-item-this"><a href=""><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> — Generate pseudo-random numbers</a></li>1126 <li class="right">1127 1128 1129 <div class="inline-search" role="search">1130 <form class="inline-search" action="../search.html" method="get">1131 <input placeholder="Quick search" aria-label="Quick search" type="search" name="q" id="search-box">1132 <input type="submit" value="Go">1133 </form>1134 </div>1135 |1136 </li>1137 <li class="right">1138<label class="theme-selector-label">1139 Theme1140 <select class="theme-selector" oninput="activateTheme(this.value)">1141 <option value="auto" selected>Auto</option>1142 <option value="light">Light</option>1143 <option value="dark">Dark</option>1144 </select>1145</label> |</li>1146 1147 </ul>1148 </div> 1149 <div class="footer">1150 © <a href="../copyright.html">Copyright</a> 2001 Python Software Foundation.1151 <br>1152 This page is licensed under the Python Software Foundation License Version 2.1153 <br>1154 Examples, recipes, and other code in the documentation are additionally licensed under the Zero Clause BSD License.1155 <br>1156 1157 See <a href="/license.html">History and License</a> for more information.<br>1158 1159 1160 <br>1161 1162 The Python Software Foundation is a non-profit corporation.1163<a href="https://www.python.org/psf/donations/">Please donate.</a>1164<br>1165 <br>1166 Last updated on Mar 10, 2026 (08:58 UTC).1167 1168 <a href="/bugs.html">Found a bug</a>?1169 1170 <br>1171 1172 Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 8.2.3.1173 </div>1174 1175 </body>1176</html>