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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="X-UA-Compatible" content="IE=Edge" /> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <title>9.6. random — Generate pseudo-random numbers — Python 2.7.16 documentation</title> <link rel="stylesheet" href="../_static/classic.css" type="text/css" /> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <script type="text/javascript" id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script> <script type="text/javascript" src="../_static/jquery.js"></script> <script type="text/javascript" src="../_static/underscore.js"></script> <script type="text/javascript" src="../_static/doctools.js"></script> <script type="text/javascript" src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within Python 2.7.16 documentation" href="../_static/opensearch.xml"/> <link rel="author" title="About these documents" href="../about.html" /> <link rel="index" title="Index" href="../genindex.html" /> <link rel="search" title="Search" href="../search.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="next" title="9.7. itertools — Functions creating iterators for efficient looping" href="itertools.html" /> <link rel="prev" title="9.5. fractions — Rational numbers" href="fractions.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <link rel="canonical" href="https://docs.python.org/2/library/random.html" /> <script type="text/javascript" src="../_static/copybutton.js"></script> </head><body> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" accesskey="I">index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="itertools.html" title="9.7. itertools — Functions creating iterators for efficient looping" accesskey="N">next</a> |</li> <li class="right" > <a href="fractions.html" title="9.5. fractions — Rational numbers" accesskey="P">previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <a href="../index.html">Python 2.7.16 documentation</a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li> <li class="nav-item nav-item-2"><a href="numeric.html" accesskey="U">9. Numeric and Mathematical Modules</a> »</li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <div class="section" id="module-random"> <span id="random-generate-pseudo-random-numbers"></span><h1>9.6. <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code></a> — Generate pseudo-random numbers<a class="headerlink" href="#module-random" title="Permalink to this headline">¶</a></h1> <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/2.7/Lib/random.py">Lib/random.py</a></p> <hr class="docutils" /> <p>This module implements pseudo-random number generators for various distributions.</p> <p>For integers, uniform selection from a range. For sequences, uniform selection of a random element, a function to generate a random permutation of a list in-place, and a function for random sampling without replacement.</p> <p>On the real line, there are functions to compute uniform, normal (Gaussian), lognormal, negative exponential, gamma, and beta distributions. For generating distributions of angles, the von Mises distribution is available.</p> <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>, which generates a random float uniformly in the semi-open range [0.0, 1.0). Python uses the Mersenne Twister as the core generator. It produces 53-bit precision floats and has a period of 2**19937-1. The underlying implementation in C is both fast and threadsafe. The Mersenne Twister is one of the most extensively tested random number generators in existence. However, being completely deterministic, it is not suitable for all purposes, and is completely unsuitable for cryptographic purposes.</p> <p>The functions supplied by this module are actually bound methods of a hidden instance of the <code class="xref py py-class docutils literal notranslate"><span class="pre">random.Random</span></code> class. You can instantiate your own instances of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> to get generators that don’t share state. This is especially useful for multi-threaded programs, creating a different instance of <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> for each thread, and using the <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jumpahead()</span></code></a> method to make it likely that the generated sequences seen by each thread don’t overlap.</p> <p>Class <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> can also be subclassed if you want to use a different basic generator of your own devising: in that case, override the <code class="xref py py-meth docutils literal notranslate"><span class="pre">random()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">seed()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">getstate()</span></code>, <code class="xref py py-meth docutils literal notranslate"><span class="pre">setstate()</span></code> and <code class="xref py py-meth docutils literal notranslate"><span class="pre">jumpahead()</span></code> methods. Optionally, a new generator can supply a <code class="xref py py-meth docutils literal notranslate"><span class="pre">getrandbits()</span></code> method — this allows <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 produce selections over an arbitrarily large range.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.4: </span>the <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> method.</p> </div> <p>As an example of subclassing, the <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code></a> module provides the <a class="reference internal" href="#random.WichmannHill" title="random.WichmannHill"><code class="xref py py-class docutils literal notranslate"><span class="pre">WichmannHill</span></code></a> class that implements an alternative generator in pure Python. The class provides a backward compatible way to reproduce results from earlier versions of Python, which used the Wichmann-Hill algorithm as the core generator. Note that this Wichmann-Hill generator can no longer be recommended: its period is too short by contemporary standards, and the sequence generated is known to fail some stringent randomness tests. See the references below for a recent variant that repairs these flaws.</p> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 2.3: </span>MersenneTwister replaced Wichmann-Hill as the default generator.</p> </div> <p>The <a class="reference internal" href="#module-random" title="random: Generate pseudo-random numbers with various common distributions."><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code></a> 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 which uses 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 numbers from sources provided by the operating system.</p> <div class="admonition warning"> <p class="first admonition-title">Warning</p> <p class="last">The pseudo-random generators of this module should not be used for security purposes. Use <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> or <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> if you require a cryptographically secure pseudo-random number generator.</p> </div> <p>Bookkeeping functions:</p> <dl class="function"> <dt id="random.seed"> <code class="descclassname">random.</code><code class="descname">seed</code><span class="sig-paren">(</span><em>a=None</em><span class="sig-paren">)</span><a class="headerlink" href="#random.seed" title="Permalink to this definition">¶</a></dt> <dd><p>Initialize internal state of the random number generator.</p> <p><code class="docutils literal notranslate"><span class="pre">None</span></code> or no argument seeds from current time or from an operating system specific randomness source if available (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 details on availability).</p> <p>If <em>a</em> is not <code class="docutils literal notranslate"><span class="pre">None</span></code> or 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> or a <a class="reference internal" href="functions.html#long" title="long"><code class="xref py py-class docutils literal notranslate"><span class="pre">long</span></code></a>, then <code class="docutils literal notranslate"><span class="pre">hash(a)</span></code> is used instead. Note that the hash values for some types are nondeterministic when <span class="target" id="index-0"></span><a class="reference internal" href="../using/cmdline.html#envvar-PYTHONHASHSEED"><code class="xref std std-envvar docutils literal notranslate"><span class="pre">PYTHONHASHSEED</span></code></a> is enabled.</p> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 2.4: </span>formerly, operating system resources were not used.</p> </div> </dd></dl> <dl class="function"> <dt id="random.getstate"> <code class="descclassname">random.</code><code class="descname">getstate</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.getstate" title="Permalink to this definition">¶</a></dt> <dd><p>Return an object capturing the current internal state of the generator. This object 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> <div class="versionadded"> <p><span class="versionmodified">New in version 2.1.</span></p> </div> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 2.6: </span>State values produced in Python 2.6 cannot be loaded into earlier versions.</p> </div> </dd></dl> <dl class="function"> <dt id="random.setstate"> <code class="descclassname">random.</code><code class="descname">setstate</code><span class="sig-paren">(</span><em>state</em><span class="sig-paren">)</span><a class="headerlink" href="#random.setstate" title="Permalink to this definition">¶</a></dt> <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>, and <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> restores the internal state of the generator to what it was at the time <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> was called.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.1.</span></p> </div> </dd></dl> <dl class="function"> <dt id="random.jumpahead"> <code class="descclassname">random.</code><code class="descname">jumpahead</code><span class="sig-paren">(</span><em>n</em><span class="sig-paren">)</span><a class="headerlink" href="#random.jumpahead" title="Permalink to this definition">¶</a></dt> <dd><p>Change the internal state to one different from and likely far away from the current state. <em>n</em> is a non-negative integer which is used to scramble the current state vector. This is most useful in multi-threaded programs, in conjunction with multiple instances of the <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> class: <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> or <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> can be used to force all instances into the same internal state, and then <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jumpahead()</span></code></a> can be used to force the instances’ states far apart.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.1.</span></p> </div> <div class="versionchanged"> <p><span class="versionmodified">Changed in version 2.3: </span>Instead of jumping to a specific state, <em>n</em> steps ahead, <code class="docutils literal notranslate"><span class="pre">jumpahead(n)</span></code> jumps to another state likely to be separated by many steps.</p> </div> </dd></dl> <dl class="function"> <dt id="random.getrandbits"> <code class="descclassname">random.</code><code class="descname">getrandbits</code><span class="sig-paren">(</span><em>k</em><span class="sig-paren">)</span><a class="headerlink" href="#random.getrandbits" title="Permalink to this definition">¶</a></dt> <dd><p>Returns a python <a class="reference internal" href="functions.html#long" title="long"><code class="xref py py-class docutils literal notranslate"><span class="pre">long</span></code></a> int with <em>k</em> random bits. This method is supplied with the MersenneTwister generator and some other generators may also provide it as an optional part of the API. When available, <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 large ranges.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.4.</span></p> </div> </dd></dl> <p>Functions for integers:</p> <dl class="function"> <dt id="random.randrange"> <code class="descclassname">random.</code><code class="descname">randrange</code><span class="sig-paren">(</span><em>stop</em><span class="sig-paren">)</span><a class="headerlink" href="#random.randrange" title="Permalink to this definition">¶</a></dt> <dt> <code class="descclassname">random.</code><code class="descname">randrange</code><span class="sig-paren">(</span><em>start</em>, <em>stop</em><span class="optional">[</span>, <em>step</em><span class="optional">]</span><span class="sig-paren">)</span></dt> <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>. This is 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>, but doesn’t actually build a range object.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 1.5.2.</span></p> </div> </dd></dl> <dl class="function"> <dt id="random.randint"> <code class="descclassname">random.</code><code class="descname">randint</code><span class="sig-paren">(</span><em>a</em>, <em>b</em><span class="sig-paren">)</span><a class="headerlink" href="#random.randint" title="Permalink to this definition">¶</a></dt> <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>.</p> </dd></dl> <p>Functions for sequences:</p> <dl class="function"> <dt id="random.choice"> <code class="descclassname">random.</code><code class="descname">choice</code><span class="sig-paren">(</span><em>seq</em><span class="sig-paren">)</span><a class="headerlink" href="#random.choice" title="Permalink to this definition">¶</a></dt> <dd><p>Return a random element from the non-empty sequence <em>seq</em>. If <em>seq</em> is empty, raises <a class="reference internal" href="exceptions.html#exceptions.IndexError" title="exceptions.IndexError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">IndexError</span></code></a>.</p> </dd></dl> <dl class="function"> <dt id="random.shuffle"> <code class="descclassname">random.</code><code class="descname">shuffle</code><span class="sig-paren">(</span><em>x</em><span class="optional">[</span>, <em>random</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.shuffle" title="Permalink to this definition">¶</a></dt> <dd><p>Shuffle the sequence <em>x</em> in place. The optional argument <em>random</em> is a 0-argument function returning a random float in [0.0, 1.0); by default, this is the 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>.</p> <p>Note that for even rather small <code class="docutils literal notranslate"><span class="pre">len(x)</span></code>, the total number of permutations of <em>x</em> is larger than the period of most random number generators; this implies that most permutations of a long sequence can never be generated.</p> </dd></dl> <dl class="function"> <dt id="random.sample"> <code class="descclassname">random.</code><code class="descname">sample</code><span class="sig-paren">(</span><em>population</em>, <em>k</em><span class="sig-paren">)</span><a class="headerlink" href="#random.sample" title="Permalink to this definition">¶</a></dt> <dd><p>Return a <em>k</em> length list of unique elements chosen from the population sequence. Used for random sampling without replacement.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.3.</span></p> </div> <p>Returns a new list containing elements from the population while leaving the original population unchanged. The resulting list is in selection order so that all sub-slices will also be valid random samples. This allows raffle winners (the sample) to be partitioned into grand prize and second place winners (the subslices).</p> <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 population contains repeats, then each occurrence is a possible selection in the sample.</p> <p>To choose a sample from a range of integers, use an <a class="reference internal" href="functions.html#xrange" title="xrange"><code class="xref py py-func docutils literal notranslate"><span class="pre">xrange()</span></code></a> object as an argument. This is especially fast and space efficient for sampling from a large population: <code class="docutils literal notranslate"><span class="pre">sample(xrange(10000000),</span> <span class="pre">60)</span></code>.</p> </dd></dl> <p>The following functions generate specific real-valued distributions. Function parameters are named after the corresponding variables in the distribution’s equation, as used in common mathematical practice; most of these equations can be found in any statistics text.</p> <dl class="function"> <dt id="random.random"> <code class="descclassname">random.</code><code class="descname">random</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.random" title="Permalink to this definition">¶</a></dt> <dd><p>Return the next random floating point number in the range [0.0, 1.0).</p> </dd></dl> <dl class="function"> <dt id="random.uniform"> <code class="descclassname">random.</code><code class="descname">uniform</code><span class="sig-paren">(</span><em>a</em>, <em>b</em><span class="sig-paren">)</span><a class="headerlink" href="#random.uniform" title="Permalink to this definition">¶</a></dt> <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> for <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> <p>The end-point value <code class="docutils literal notranslate"><span class="pre">b</span></code> may or may not be included in the range depending on floating-point rounding in the equation <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> </dd></dl> <dl class="function"> <dt id="random.triangular"> <code class="descclassname">random.</code><code class="descname">triangular</code><span class="sig-paren">(</span><em>low</em>, <em>high</em>, <em>mode</em><span class="sig-paren">)</span><a class="headerlink" href="#random.triangular" title="Permalink to this definition">¶</a></dt> <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> and with the specified <em>mode</em> between those bounds. The <em>low</em> and <em>high</em> bounds default to zero and one. The <em>mode</em> argument defaults to the midpoint between the bounds, giving a symmetric distribution.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.6.</span></p> </div> </dd></dl> <dl class="function"> <dt id="random.betavariate"> <code class="descclassname">random.</code><code class="descname">betavariate</code><span class="sig-paren">(</span><em>alpha</em>, <em>beta</em><span class="sig-paren">)</span><a class="headerlink" href="#random.betavariate" title="Permalink to this definition">¶</a></dt> <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> and <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> </dd></dl> <dl class="function"> <dt id="random.expovariate"> <code class="descclassname">random.</code><code class="descname">expovariate</code><span class="sig-paren">(</span><em>lambd</em><span class="sig-paren">)</span><a class="headerlink" href="#random.expovariate" title="Permalink to this definition">¶</a></dt> <dd><p>Exponential distribution. <em>lambd</em> is 1.0 divided by the desired mean. It should be nonzero. (The parameter would be called “lambda”, but that is a reserved word in Python.) Returned values range from 0 to positive infinity if <em>lambd</em> is positive, and from negative infinity to 0 if <em>lambd</em> is negative.</p> </dd></dl> <dl class="function"> <dt id="random.gammavariate"> <code class="descclassname">random.</code><code class="descname">gammavariate</code><span class="sig-paren">(</span><em>alpha</em>, <em>beta</em><span class="sig-paren">)</span><a class="headerlink" href="#random.gammavariate" title="Permalink to this definition">¶</a></dt> <dd><p>Gamma distribution. (<em>Not</em> the gamma function!) 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> and <code class="docutils literal notranslate"><span class="pre">beta</span> <span class="pre">></span> <span class="pre">0</span></code>.</p> <p>The probability distribution function is:</p> <div class="highlight-default 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> <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> <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> </pre></div> </div> </dd></dl> <dl class="function"> <dt id="random.gauss"> <code class="descclassname">random.</code><code class="descname">gauss</code><span class="sig-paren">(</span><em>mu</em>, <em>sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#random.gauss" title="Permalink to this definition">¶</a></dt> <dd><p>Gaussian distribution. <em>mu</em> is the mean, and <em>sigma</em> is the standard deviation. This is slightly faster than the <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> </dd></dl> <dl class="function"> <dt id="random.lognormvariate"> <code class="descclassname">random.</code><code class="descname">lognormvariate</code><span class="sig-paren">(</span><em>mu</em>, <em>sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#random.lognormvariate" title="Permalink to this definition">¶</a></dt> <dd><p>Log normal distribution. If you take the natural logarithm of this distribution, you’ll get a normal distribution with mean <em>mu</em> and standard deviation <em>sigma</em>. <em>mu</em> can have any value, and <em>sigma</em> must be greater than zero.</p> </dd></dl> <dl class="function"> <dt id="random.normalvariate"> <code class="descclassname">random.</code><code class="descname">normalvariate</code><span class="sig-paren">(</span><em>mu</em>, <em>sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#random.normalvariate" title="Permalink to this definition">¶</a></dt> <dd><p>Normal distribution. <em>mu</em> is the mean, and <em>sigma</em> is the standard deviation.</p> </dd></dl> <dl class="function"> <dt id="random.vonmisesvariate"> <code class="descclassname">random.</code><code class="descname">vonmisesvariate</code><span class="sig-paren">(</span><em>mu</em>, <em>kappa</em><span class="sig-paren">)</span><a class="headerlink" href="#random.vonmisesvariate" title="Permalink to this definition">¶</a></dt> <dd><p><em>mu</em> is the mean angle, expressed in radians between 0 and 2*<em>pi</em>, and <em>kappa</em> is the concentration parameter, which must be greater than or equal to zero. If <em>kappa</em> is equal to zero, this distribution reduces to a uniform random angle over the range 0 to 2*<em>pi</em>.</p> </dd></dl> <dl class="function"> <dt id="random.paretovariate"> <code class="descclassname">random.</code><code class="descname">paretovariate</code><span class="sig-paren">(</span><em>alpha</em><span class="sig-paren">)</span><a class="headerlink" href="#random.paretovariate" title="Permalink to this definition">¶</a></dt> <dd><p>Pareto distribution. <em>alpha</em> is the shape parameter.</p> </dd></dl> <dl class="function"> <dt id="random.weibullvariate"> <code class="descclassname">random.</code><code class="descname">weibullvariate</code><span class="sig-paren">(</span><em>alpha</em>, <em>beta</em><span class="sig-paren">)</span><a class="headerlink" href="#random.weibullvariate" title="Permalink to this definition">¶</a></dt> <dd><p>Weibull distribution. <em>alpha</em> is the scale parameter and <em>beta</em> is the shape parameter.</p> </dd></dl> <p>Alternative Generators:</p> <dl class="class"> <dt id="random.WichmannHill"> <em class="property">class </em><code class="descclassname">random.</code><code class="descname">WichmannHill</code><span class="sig-paren">(</span><span class="optional">[</span><em>seed</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.WichmannHill" title="Permalink to this definition">¶</a></dt> <dd><p>Class that implements the Wichmann-Hill algorithm as the core generator. Has all of the same methods as <code class="xref py py-class docutils literal notranslate"><span class="pre">Random</span></code> plus the <a class="reference internal" href="#random.whseed" title="random.whseed"><code class="xref py py-meth docutils literal notranslate"><span class="pre">whseed()</span></code></a> method described below. Because this class is implemented in pure Python, it is not threadsafe and may require locks between calls. The period of the generator is 6,953,607,871,644 which is small enough to require care that two independent random sequences do not overlap.</p> </dd></dl> <dl class="function"> <dt id="random.whseed"> <code class="descclassname">random.</code><code class="descname">whseed</code><span class="sig-paren">(</span><span class="optional">[</span><em>x</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.whseed" title="Permalink to this definition">¶</a></dt> <dd><p>This is obsolete, supplied for bit-level compatibility with versions of Python prior to 2.1. See <a class="reference internal" href="#random.seed" title="random.seed"><code class="xref py py-func docutils literal notranslate"><span class="pre">seed()</span></code></a> for details. <a class="reference internal" href="#random.whseed" title="random.whseed"><code class="xref py py-func docutils literal notranslate"><span class="pre">whseed()</span></code></a> does not guarantee that distinct integer arguments yield distinct internal states, and can yield no more than about 2**24 distinct internal states in all.</p> </dd></dl> <dl class="class"> <dt id="random.SystemRandom"> <em class="property">class </em><code class="descclassname">random.</code><code class="descname">SystemRandom</code><span class="sig-paren">(</span><span class="optional">[</span><em>seed</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.SystemRandom" title="Permalink to this definition">¶</a></dt> <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 numbers from sources provided by the operating system. Not available on all systems. Does not rely on software state and sequences are not reproducible. Accordingly, 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> and <a class="reference internal" href="#random.jumpahead" title="random.jumpahead"><code class="xref py py-meth docutils literal notranslate"><span class="pre">jumpahead()</span></code></a> methods have no effect and are ignored. 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> 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 raise <a class="reference internal" href="exceptions.html#exceptions.NotImplementedError" title="exceptions.NotImplementedError"><code class="xref py py-exc docutils literal notranslate"><span class="pre">NotImplementedError</span></code></a> if called.</p> <div class="versionadded"> <p><span class="versionmodified">New in version 2.4.</span></p> </div> </dd></dl> <p>Examples of basic usage:</p> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span> <span class="c1"># Random float x, 0.0 <= x < 1.0</span> <span class="go">0.37444887175646646</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="c1"># Random float x, 1.0 <= x < 10.0</span> <span class="go">1.1800146073117523</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="c1"># Integer from 1 to 10, endpoints included</span> <span class="go">7</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</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</span> <span class="go">26</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="s1">'abcdefghij'</span><span class="p">)</span> <span class="c1"># Choose a random element</span> <span class="go">'c'</span> <span class="gp">>>> </span><span class="n">items</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">]</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">items</span><span class="p">)</span> <span class="gp">>>> </span><span class="n">items</span> <span class="go">[7, 3, 2, 5, 6, 4, 1]</span> <span class="gp">>>> </span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">],</span> <span class="mi">3</span><span class="p">)</span> <span class="c1"># Choose 3 elements</span> <span class="go">[4, 1, 5]</span> </pre></div> </div> <div class="admonition seealso"> <p class="first admonition-title">See also</p> <p>M. Matsumoto and T. Nishimura, “Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator”, ACM Transactions on Modeling and Computer Simulation Vol. 8, No. 1, January pp.3–30 1998.</p> <p>Wichmann, B. A. & Hill, I. D., “Algorithm AS 183: An efficient and portable pseudo-random number generator”, Applied Statistics 31 (1982) 188-190.</p> <p class="last"><a class="reference external" href="http://code.activestate.com/recipes/576707/">Complementary-Multiply-with-Carry recipe</a> for a compatible alternative random number generator with a long period and comparatively simple update operations.</p> </div> </div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <h4>Previous topic</h4> <p class="topless"><a href="fractions.html" title="previous chapter">9.5. <code class="docutils literal notranslate"><span class="pre">fractions</span></code> — Rational numbers</a></p> <h4>Next topic</h4> <p class="topless"><a href="itertools.html" title="next chapter">9.7. <code class="docutils literal notranslate"><span class="pre">itertools</span></code> — Functions creating iterators for efficient looping</a></p> <div role="note" aria-label="source link"> <h3>This Page</h3> <ul class="this-page-menu"> <li><a href="../_sources/library/random.rst.txt" rel="nofollow">Show Source</a></li> </ul> </div> <div id="searchbox" style="display: none" role="search"> <h3>Quick search</h3> <div class="searchformwrapper"> <form class="search" action="../search.html" method="get"> <input type="text" name="q" /> <input type="submit" value="Go" /> <input type="hidden" name="check_keywords" value="yes" /> <input type="hidden" name="area" value="default" /> </form> </div> </div> <script type="text/javascript">$('#searchbox').show(0);</script> </div> </div> <div class="clearer"></div> </div> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" >index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="itertools.html" title="9.7. itertools — Functions creating iterators for efficient looping" >next</a> |</li> <li class="right" > <a href="fractions.html" title="9.5. fractions — Rational numbers" >previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <a href="../index.html">Python 2.7.16 documentation</a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li> <li class="nav-item nav-item-2"><a href="numeric.html" >9. 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