klarkxy/hustoj
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
master
hustoj/web/python-docs/library/random.html
klarkxy 723430cade 增加python文档
2025-03-09 17:10:56 +08:00

631 lines
66 KiB
HTML
Raw Permalink Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="zh_CN">
<head>
<meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
<title>random --- 生成伪随机数 &#8212; Python 3.8.20 文档</title><meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="../_static/pydoctheme.css" type="text/css" />
<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
<script id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script>
<script src="../_static/jquery.js"></script>
<script src="../_static/underscore.js"></script>
<script src="../_static/doctools.js"></script>
<script src="../_static/language_data.js"></script>
<script src="../_static/translations.js"></script>
<script src="../_static/sidebar.js"></script>
<link rel="search" type="application/opensearchdescription+xml"
title="在 Python 3.8.20 文档 中搜索"
href="../_static/opensearch.xml"/>
<link rel="author" title="关于这些文档" href="../about.html" />
<link rel="index" title="索引" href="../genindex.html" />
<link rel="search" title="搜索" href="../search.html" />
<link rel="copyright" title="版权所有" href="../copyright.html" />
<link rel="next" title="statistics --- 数学统计函数" href="statistics.html" />
<link rel="prev" title="fractions --- 分数" href="fractions.html" />
<link rel="canonical" href="https://docs.python.org/3/library/random.html" />
<style>
@media only screen {
table.full-width-table {
width: 100%;
}
}
</style>
<link rel="shortcut icon" type="image/png" href="../_static/py.svg" />
<script type="text/javascript" src="../_static/copybutton.js"></script>
<script type="text/javascript" src="../_static/menu.js"></script>
</head>
<body>
<div class="mobile-nav">
<input type="checkbox" id="menuToggler" class="toggler__input" aria-controls="navigation"
aria-pressed="false" aria-expanded="false" role="button" aria-label="Menu" />
<label for="menuToggler" class="toggler__label">
<span></span>
</label>
<nav class="nav-content" role="navigation">
<a href="https://www.python.org/" class="nav-logo">
<img src="../_static/py.svg" alt="Logo"/>
</a>
<div class="version_switcher_placeholder"></div>
<form role="search" class="search" action="../search.html" method="get">
<svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" class="search-icon">
<path fill-rule="nonzero"
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" fill="#444"></path>
</svg>
<input type="text" name="q" aria-label="快速搜索"/>
<input type="submit" value="转向"/>
</form>
</nav>
<div class="menu-wrapper">
<nav class="menu" role="navigation" aria-label="main navigation">
<div class="language_switcher_placeholder"></div>
<h3><a href="../contents.html">目录</a></h3>
<ul>
<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> --- 生成伪随机数</a><ul>
<li><a class="reference internal" href="#bookkeeping-functions">簿记功能</a></li>
<li><a class="reference internal" href="#functions-for-integers">整数用函数</a></li>
<li><a class="reference internal" href="#functions-for-sequences">序列用函数</a></li>
<li><a class="reference internal" href="#real-valued-distributions">实值分布</a></li>
<li><a class="reference internal" href="#alternative-generator">替代生成器</a></li>
<li><a class="reference internal" href="#notes-on-reproducibility">关于再现性的说明</a></li>
<li><a class="reference internal" href="#examples-and-recipes">例子和配方</a></li>
</ul>
</li>
</ul>
<h4>上一个主题</h4>
<p class="topless"><a href="fractions.html"
title="上一章"><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code> --- 分数</a></p>
<h4>下一个主题</h4>
<p class="topless"><a href="statistics.html"
title="下一章"><code class="xref py py-mod docutils literal notranslate"><span class="pre">statistics</span></code> --- 数学统计函数</a></p>
<div role="note" aria-label="source link">
<h3>本页</h3>
<ul class="this-page-menu">
<li><a href="../bugs.html">报告 Bug</a></li>
<li>
<a href="https://github.com/python/cpython/blob/3.8/Doc/library/random.rst"
rel="nofollow">显示源代码
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
<div id="outdated-warning" style="padding: .5em; text-align: center; background-color: #FFBABA; color: #6A0E0E;">
这个文档所针对的是一个已不再受支持的 Python 旧版本。
你应当升级版本，并阅读
<a href="/3/library/random.html"> Python 当前稳定版本的文档</a>.
</div>
<div class="related" role="navigation" aria-label="related navigation">
<h3>导航</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="总目录"
accesskey="I">索引</a></li>
<li class="right" >
<a href="../py-modindex.html" title="Python 模块索引"
>模块</a> |</li>
<li class="right" >
<a href="statistics.html" title="statistics --- 数学统计函数"
accesskey="N">下一页</a> |</li>
<li class="right" >
<a href="fractions.html" title="fractions --- 分数"
accesskey="P">上一页</a> |</li>
<li><img src="../_static/py.svg" alt="python logo" style="vertical-align: middle; margin-top: -1px"/></li>
<li><a href="https://www.python.org/">Python</a> &#187;</li>
<li class="switchers">
<div class="language_switcher_placeholder"></div>
<div class="version_switcher_placeholder"></div>
</li>
<li>
</li>
<li id="cpython-language-and-version">
<a href="../index.html">3.8.20 Documentation</a> &#187;
</li>
<li class="nav-item nav-item-1"><a href="index.html" >Python 标准库</a> &#187;</li>
<li class="nav-item nav-item-2"><a href="numeric.html" accesskey="U">数字和数学模块</a> &#187;</li>
<li class="right">
<div class="inline-search" role="search">
<form class="inline-search" action="../search.html" method="get">
<input placeholder="快速搜索" aria-label="快速搜索" type="text" name="q" />
<input type="submit" value="转向" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
|
</li>
</ul>
</div>
<div class="document">
<div class="documentwrapper">
<div class="bodywrapper">
<div class="body" role="main">
<section id="module-random">
<span id="random-generate-pseudo-random-numbers"></span><h1><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> --- 生成伪随机数<a class="headerlink" href="#module-random" title="永久链接至标题"></a></h1>
<p><strong>源码：</strong> <a class="reference external" href="https://github.com/python/cpython/tree/3.8/Lib/random.py">Lib/random.py</a></p>
<hr class="docutils" />
<p>该模块实现了各种分布的伪随机数生成器。</p>
<p>对于整数，从范围中有统一的选择。 对于序列，存在随机元素的统一选择、用于生成列表的随机排列的函数、以及用于随机抽样而无需替换的函数。</p>
<p>在实数轴上，有计算均匀、正态（高斯）、对数正态、负指数、伽马和贝塔分布的函数。 为了生成角度分布，可以使用 von Mises 分布。</p>
<p>几乎所有模块函数都依赖于基本函数 <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> ，它在半开放区间 [0.0,1.0) 内均匀生成随机浮点数。 Python 使用 Mersenne Twister 作为核心生成器。 它产生 53 位精度浮点数，周期为 2**19937-1 ，其在 C 中的底层实现既快又线程安全。 Mersenne Twister 是现存最广泛测试的随机数发生器之一。 但是，因为完全确定性，它不适用于所有目的，并且完全不适合加密目的。</p>
<p>这个模块提供的函数实际上是 <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> 类的隐藏实例的绑定方法。 你可以实例化自己的 <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> 类实例以获取不共享状态的生成器。</p>
<p>如果你想使用自己设计的不同基础生成器，类 <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> 也可以作为子类：在这种情况下，重载 <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> 以及 <code class="xref py py-meth docutils literal notranslate"><span class="pre">setstate()</span></code> 方法。可选地，新生成器可以提供 <code class="xref py py-meth docutils literal notranslate"><span class="pre">getrandbits()</span></code> 方法——这允许 <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> 在任意大的范围内产生选择。</p>
<p><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> 模块还提供 <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> 类，它使用系统函数 <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> 从操作系统提供的源生成随机数。</p>
<div class="admonition warning">
<p class="admonition-title">警告</p>
<p>不应将此模块的伪随机生成器用于安全目的。 有关安全性或加密用途，请参阅 <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> 模块。</p>
</div>
<div class="admonition seealso">
<p class="admonition-title">参见</p>
<p>M. Matsumoto and T. Nishimura, &quot;Mersenne Twister: A 623-dimensionally
equidistributed uniform pseudorandom number generator&quot;, ACM Transactions on
Modeling and Computer Simulation Vol. 8, No. 1, January pp.3--30 1998.</p>
<p><a class="reference external" href="https://code.activestate.com/recipes/576707/">Complementary-Multiply-with-Carry recipe</a> 用于兼容的替代随机数发生器，具有长周期和相对简单的更新操作。</p>
</div>
<section id="bookkeeping-functions">
<h2>簿记功能<a class="headerlink" href="#bookkeeping-functions" title="永久链接至标题"></a></h2>
<dl class="function">
<dt id="random.seed">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">seed</code><span class="sig-paren">(</span><em class="sig-param">a=None</em>, <em class="sig-param">version=2</em><span class="sig-paren">)</span><a class="headerlink" href="#random.seed" title="永久链接至目标"></a></dt>
<dd><p>初始化随机数生成器。</p>
<p>如果 <em>a</em> 被省略或为 <code class="docutils literal notranslate"><span class="pre">None</span></code> ，则使用当前系统时间。 如果操作系统提供随机源，则使用它们而不是系统时间（有关可用性的详细信息，请参阅 <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> 函数）。</p>
<p>如果 <em>a</em> 是 int 类型，则直接使用。</p>
<p>对于版本2（默认的），<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> 或 <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> 对象转换为 <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> 并使用它的所有位。</p>
<p>对于版本1（用于从旧版本的Python再现随机序列），用于 <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> 和 <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> 的算法生成更窄的种子范围。</p>
<div class="versionchanged">
<p><span class="versionmodified changed">在 3.2 版更改: </span>已移至版本2方案，该方案使用字符串种子中的所有位。</p>
</div>
</dd></dl>
<dl class="function">
<dt id="random.getstate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">getstate</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.getstate" title="永久链接至目标"></a></dt>
<dd><p>返回捕获生成器当前内部状态的对象。 这个对象可以传递给 <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> 来恢复状态。</p>
</dd></dl>
<dl class="function">
<dt id="random.setstate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">setstate</code><span class="sig-paren">(</span><em class="sig-param">state</em><span class="sig-paren">)</span><a class="headerlink" href="#random.setstate" title="永久链接至目标"></a></dt>
<dd><p><em>state</em> 应该是从之前调用 <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> 获得的，并且 <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> 将生成器的内部状态恢复到 <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> 被调用时的状态。</p>
</dd></dl>
<dl class="function">
<dt id="random.getrandbits">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">getrandbits</code><span class="sig-paren">(</span><em class="sig-param">k</em><span class="sig-paren">)</span><a class="headerlink" href="#random.getrandbits" title="永久链接至目标"></a></dt>
<dd><p>返回具有 <em>k</em> 个随机比特位的 Python 整数。 此方法随 Mersenne Twister 生成器一起提供，其他一些生成器也可能将其作为 API 的可选部分提供。 在可能的情况下，<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> 会启用 <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> 来处理任意大的区间。</p>
</dd></dl>
</section>
<section id="functions-for-integers">
<h2>整数用函数<a class="headerlink" href="#functions-for-integers" title="永久链接至标题"></a></h2>
<dl class="function">
<dt id="random.randrange">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">randrange</code><span class="sig-paren">(</span><em class="sig-param">stop</em><span class="sig-paren">)</span><a class="headerlink" href="#random.randrange" title="永久链接至目标"></a></dt>
<dt>
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">randrange</code><span class="sig-paren">(</span><em class="sig-param">start</em>, <em class="sig-param">stop</em><span class="optional">[</span>, <em class="sig-param">step</em><span class="optional">]</span><span class="sig-paren">)</span></dt>
<dd><p>从 <code class="docutils literal notranslate"><span class="pre">range(start,</span> <span class="pre">stop,</span> <span class="pre">step)</span></code> 返回一个随机选择的元素。 这相当于 <code class="docutils literal notranslate"><span class="pre">choice(range(start,</span> <span class="pre">stop,</span> <span class="pre">step))</span></code> ，但实际上并没有构建一个 range 对象。</p>
<p>位置参数模式匹配 <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> 。不应使用关键字参数，因为该函数可能以意外的方式使用它们。</p>
<div class="versionchanged">
<p><span class="versionmodified changed">在 3.2 版更改: </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> 在生成均匀分布的值方面更为复杂。 以前它使用了像``int(random()*n)``这样的形式，它可以产生稍微不均匀的分布。</p>
</div>
</dd></dl>
<dl class="function">
<dt id="random.randint">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">randint</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="headerlink" href="#random.randint" title="永久链接至目标"></a></dt>
<dd><p>返回随机整数 <em>N</em> 满足 <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">N</span> <span class="pre">&lt;=</span> <span class="pre">b</span></code>。相当于 <code class="docutils literal notranslate"><span class="pre">randrange(a,</span> <span class="pre">b+1)</span></code>。</p>
</dd></dl>
</section>
<section id="functions-for-sequences">
<h2>序列用函数<a class="headerlink" href="#functions-for-sequences" title="永久链接至标题"></a></h2>
<dl class="function">
<dt id="random.choice">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">choice</code><span class="sig-paren">(</span><em class="sig-param">seq</em><span class="sig-paren">)</span><a class="headerlink" href="#random.choice" title="永久链接至目标"></a></dt>
<dd><p>从非空序列 <em>seq</em> 返回一个随机元素。 如果 <em>seq</em> 为空，则引发 <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>
</dd></dl>
<dl class="function">
<dt id="random.choices">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">choices</code><span class="sig-paren">(</span><em class="sig-param">population</em>, <em class="sig-param">weights=None</em>, <em class="sig-param">*</em>, <em class="sig-param">cum_weights=None</em>, <em class="sig-param">k=1</em><span class="sig-paren">)</span><a class="headerlink" href="#random.choices" title="永久链接至目标"></a></dt>
<dd><p>从 <em>population</em> 中有重复地随机选取元素，返回大小为 <em>k</em> 的元素列表。 如果 <em>population</em> 为空，则引发 <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>
<p>如果指定了 <em>weight</em> 序列，则根据相对权重进行选择。 或者，如果给出 <em>cum_weights</em> 序列，则根据累积权重（可能使用 <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> 计算）进行选择。 例如，相对权重``[10, 5, 30, 5]``相当于累积权重``[10, 15, 45, 50]``。 在内部，相对权重在进行选择之前会转换为累积权重，因此提供累积权重可以节省工作量。</p>
<p>如果既未指定 <em>weight</em> 也未指定 <em>cum_weights</em> ，则以相等的概率进行选择。 如果提供了权重序列，则它必须与 <em>population</em> 序列的长度相同。 一个 <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> 指定了 <em>weights</em> 和*cum_weights*。</p>
<p><em>weights</em> 或 <em>cum_weights</em> 可以使用任何与 <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> 所返回的 <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> 值互操作的数值类型（包括整数、浮点数和分数但不包括十进制小数）。 权重假定为非负数。</p>
<p>对于给定的种子，具有相等加权的 <a class="reference internal" href="#random.choices" title="random.choices"><code class="xref py py-func docutils literal notranslate"><span class="pre">choices()</span></code></a> 函数通常产生与重复调用 <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> 不同的序列。 <a class="reference internal" href="#random.choices" title="random.choices"><code class="xref py py-func docutils literal notranslate"><span class="pre">choices()</span></code></a> 使用的算法使用浮点运算来实现内部一致性和速度。 <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> 使用的算法默认为重复选择的整数运算，以避免因舍入误差引起的小偏差。</p>
<div class="versionadded">
<p><span class="versionmodified added">3.6 新版功能.</span></p>
</div>
</dd></dl>
<dl class="function">
<dt id="random.shuffle">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">shuffle</code><span class="sig-paren">(</span><em class="sig-param">x</em><span class="optional">[</span>, <em class="sig-param">random</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.shuffle" title="永久链接至目标"></a></dt>
<dd><p>将序列 <em>x</em> 随机打乱位置。</p>
<p>可选参数 <em>random</em> 是一个0参数函数，在 [0.0, 1.0) 中返回随机浮点数；默认情况下，这是函数 <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>要改变一个不可变的序列并返回一个新的打乱列表，请使用``sample(x, k=len(x))``。</p>
<p>请注意，即使对于小的 <code class="docutils literal notranslate"><span class="pre">len(x)</span></code>，<em>x</em> 的排列总数也可以快速增长，大于大多数随机数生成器的周期。 这意味着长序列的大多数排列永远不会产生。 例如，长度为2080的序列是可以在 Mersenne Twister 随机数生成器的周期内拟合的最大序列。</p>
</dd></dl>
<dl class="function">
<dt id="random.sample">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">sample</code><span class="sig-paren">(</span><em class="sig-param">population</em>, <em class="sig-param">k</em><span class="sig-paren">)</span><a class="headerlink" href="#random.sample" title="永久链接至目标"></a></dt>
<dd><p>返回从总体序列或集合中选择的唯一元素的 <em>k</em> 长度列表。 用于无重复的随机抽样。</p>
<p>返回包含来自总体的元素的新列表，同时保持原始总体不变。 结果列表按选择顺序排列，因此所有子切片也将是有效的随机样本。 这允许抽奖获奖者（样本）被划分为大奖和第二名获胜者（子切片）。</p>
<p>总体成员不必是 <a class="reference internal" href="../glossary.html#term-hashable"><span class="xref std std-term">hashable</span></a> 或 unique 。 如果总体包含重复，则每次出现都是样本中可能的选择。</p>
<p>要从一系列整数中选择样本，请使用 <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> 对象作为参数。 对于从大量人群中采样，这种方法特别快速且节省空间：<code class="docutils literal notranslate"><span class="pre">sample(range(10000000),</span> <span class="pre">k=60)</span></code> 。</p>
<p>如果样本大小大于总体大小，则引发 <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> 。</p>
</dd></dl>
</section>
<section id="real-valued-distributions">
<h2>实值分布<a class="headerlink" href="#real-valued-distributions" title="永久链接至标题"></a></h2>
<p>以下函数生成特定的实值分布。如常用数学实践中所使用的那样, 函数参数以分布方程中的相应变量命名;大多数这些方程都可以在任何统计学教材中找到。</p>
<dl class="function">
<dt id="random.random">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">random</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#random.random" title="永久链接至目标"></a></dt>
<dd><p>返回 [0.0, 1.0) 范围内的下一个随机浮点数。</p>
</dd></dl>
<dl class="function">
<dt id="random.uniform">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">uniform</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em><span class="sig-paren">)</span><a class="headerlink" href="#random.uniform" title="永久链接至目标"></a></dt>
<dd><p>返回一个随机浮点数 <em>N</em> ，当 <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">b</span></code> 时 <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">N</span> <span class="pre">&lt;=</span> <span class="pre">b</span></code> ，当 <code class="docutils literal notranslate"><span class="pre">b</span> <span class="pre">&lt;</span> <span class="pre">a</span></code> 时 <code class="docutils literal notranslate"><span class="pre">b</span> <span class="pre">&lt;=</span> <span class="pre">N</span> <span class="pre">&lt;=</span> <span class="pre">a</span></code> 。</p>
<p>取决于等式 <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> 中的浮点舍入，终点 <code class="docutils literal notranslate"><span class="pre">b</span></code> 可以包括或不包括在该范围内。</p>
</dd></dl>
<dl class="function">
<dt id="random.triangular">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">triangular</code><span class="sig-paren">(</span><em class="sig-param">low</em>, <em class="sig-param">high</em>, <em class="sig-param">mode</em><span class="sig-paren">)</span><a class="headerlink" href="#random.triangular" title="永久链接至目标"></a></dt>
<dd><p>返回一个随机浮点数 <em>N</em> ，使得 <code class="docutils literal notranslate"><span class="pre">low</span> <span class="pre">&lt;=</span> <span class="pre">N</span> <span class="pre">&lt;=</span> <span class="pre">high</span></code> 并在这些边界之间使用指定的 <em>mode</em> 。 <em>low</em> 和 <em>high</em> 边界默认为零和一。 <em>mode</em> 参数默认为边界之间的中点，给出对称分布。</p>
</dd></dl>
<dl class="function">
<dt id="random.betavariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">betavariate</code><span class="sig-paren">(</span><em class="sig-param">alpha</em>, <em class="sig-param">beta</em><span class="sig-paren">)</span><a class="headerlink" href="#random.betavariate" title="永久链接至目标"></a></dt>
<dd><p>Beta 分布。 参数的条件是 <code class="docutils literal notranslate"><span class="pre">alpha</span> <span class="pre">&gt;</span> <span class="pre">0</span></code> 和 <code class="docutils literal notranslate"><span class="pre">beta</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>。 返回值的范围介于 0 和 1 之间。</p>
</dd></dl>
<dl class="function">
<dt id="random.expovariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">expovariate</code><span class="sig-paren">(</span><em class="sig-param">lambd</em><span class="sig-paren">)</span><a class="headerlink" href="#random.expovariate" title="永久链接至目标"></a></dt>
<dd><p>指数分布。 <em>lambd</em> 是 1.0 除以所需的平均值，它应该是非零的。 （该参数本应命名为 “lambda” ，但这是 Python 中的保留字。）如果 <em>lambd</em> 为正，则返回值的范围为 0 到正无穷大；如果 <em>lambd</em> 为负，则返回值从负无穷大到 0。</p>
</dd></dl>
<dl class="function">
<dt id="random.gammavariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">gammavariate</code><span class="sig-paren">(</span><em class="sig-param">alpha</em>, <em class="sig-param">beta</em><span class="sig-paren">)</span><a class="headerlink" href="#random.gammavariate" title="永久链接至目标"></a></dt>
<dd><p>Gamma 分布。 （ <em>不是</em> gamma 函数！ ） 参数的条件是 <code class="docutils literal notranslate"><span class="pre">alpha</span> <span class="pre">&gt;</span> <span class="pre">0</span></code> 和 <code class="docutils literal notranslate"><span class="pre">beta</span> <span class="pre">&gt;</span> <span class="pre">0</span></code>。</p>
<p>概率分布函数是:</p>
<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>
<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="sig-prename descclassname">random.</code><code class="sig-name descname">gauss</code><span class="sig-paren">(</span><em class="sig-param">mu</em>, <em class="sig-param">sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#random.gauss" title="永久链接至目标"></a></dt>
<dd><p>高斯分布。 <em>mu</em> 是平均值，<em>sigma</em> 是标准差。 这比下面定义的 <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> 函数略快。</p>
</dd></dl>
<dl class="function">
<dt id="random.lognormvariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">lognormvariate</code><span class="sig-paren">(</span><em class="sig-param">mu</em>, <em class="sig-param">sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#random.lognormvariate" title="永久链接至目标"></a></dt>
<dd><p>对数正态分布。 如果你采用这个分布的自然对数，你将得到一个正态分布，平均值为 <em>mu</em> 和标准差为 <em>sigma</em> 。 <em>mu</em> 可以是任何值，<em>sigma</em> 必须大于零。</p>
</dd></dl>
<dl class="function">
<dt id="random.normalvariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">normalvariate</code><span class="sig-paren">(</span><em class="sig-param">mu</em>, <em class="sig-param">sigma</em><span class="sig-paren">)</span><a class="headerlink" href="#random.normalvariate" title="永久链接至目标"></a></dt>
<dd><p>正态分布。 <em>mu</em> 是平均值，<em>sigma</em> 是标准差。</p>
</dd></dl>
<dl class="function">
<dt id="random.vonmisesvariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">vonmisesvariate</code><span class="sig-paren">(</span><em class="sig-param">mu</em>, <em class="sig-param">kappa</em><span class="sig-paren">)</span><a class="headerlink" href="#random.vonmisesvariate" title="永久链接至目标"></a></dt>
<dd><p>冯·米塞斯分布。 <em>mu</em> 是平均角度，以弧度表示，介于0和 2*<em>pi</em> 之间，<em>kappa</em> 是浓度参数，必须大于或等于零。 如果 <em>kappa</em> 等于零，则该分布在 0 到 2*<em>pi</em> 的范围内减小到均匀的随机角度。</p>
</dd></dl>
<dl class="function">
<dt id="random.paretovariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">paretovariate</code><span class="sig-paren">(</span><em class="sig-param">alpha</em><span class="sig-paren">)</span><a class="headerlink" href="#random.paretovariate" title="永久链接至目标"></a></dt>
<dd><p>帕累托分布。 <em>alpha</em> 是形状参数。</p>
</dd></dl>
<dl class="function">
<dt id="random.weibullvariate">
<code class="sig-prename descclassname">random.</code><code class="sig-name descname">weibullvariate</code><span class="sig-paren">(</span><em class="sig-param">alpha</em>, <em class="sig-param">beta</em><span class="sig-paren">)</span><a class="headerlink" href="#random.weibullvariate" title="永久链接至目标"></a></dt>
<dd><p>威布尔分布。 <em>alpha</em> 是比例参数，<em>beta</em> 是形状参数。</p>
</dd></dl>
</section>
<section id="alternative-generator">
<h2>替代生成器<a class="headerlink" href="#alternative-generator" title="永久链接至标题"></a></h2>
<dl class="class">
<dt id="random.Random">
<em class="property">class </em><code class="sig-prename descclassname">random.</code><code class="sig-name descname">Random</code><span class="sig-paren">(</span><span class="optional">[</span><em class="sig-param">seed</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.Random" title="永久链接至目标"></a></dt>
<dd><p>该类实现了 <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> 模块所用的默认伪随机数生成器。</p>
</dd></dl>
<dl class="class">
<dt id="random.SystemRandom">
<em class="property">class </em><code class="sig-prename descclassname">random.</code><code class="sig-name descname">SystemRandom</code><span class="sig-paren">(</span><span class="optional">[</span><em class="sig-param">seed</em><span class="optional">]</span><span class="sig-paren">)</span><a class="headerlink" href="#random.SystemRandom" title="永久链接至目标"></a></dt>
<dd><p>使用 <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> 函数的类，用从操作系统提供的源生成随机数。 这并非适用于所有系统。 也不依赖于软件状态，序列不可重现。 因此，<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> 方法没有效果而被忽略。 <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> 和 <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> 方法如果被调用则引发 <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>。</p>
</dd></dl>
</section>
<section id="notes-on-reproducibility">
<h2>关于再现性的说明<a class="headerlink" href="#notes-on-reproducibility" title="永久链接至标题"></a></h2>
<p>有时能够重现伪随机数生成器给出的序列是有用的。 通过重新使用种子值，只要多个线程没有运行，相同的序列就可以在两次不同运行之间重现。</p>
<p>大多数随机模块的算法和种子函数都会在 Python 版本中发生变化，但保证两个方面不会改变：</p>
<ul class="simple">
<li><p>如果添加了新的播种方法，则将提供向后兼容的播种机。</p></li>
<li><p>当兼容的播种机被赋予相同的种子时，生成器的 <code class="xref py py-meth docutils literal notranslate"><span class="pre">random()</span></code> 方法将继续产生相同的序列。</p></li>
</ul>
</section>
<section id="examples-and-recipes">
<span id="random-examples"></span><h2>例子和配方<a class="headerlink" href="#examples-and-recipes" title="永久链接至标题"></a></h2>
<p>基本示例:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">random</span><span class="p">()</span> <span class="c1"># Random float: 0.0 &lt;= x &lt; 1.0</span>
<span class="go">0.37444887175646646</span>
<span class="gp">&gt;&gt;&gt; </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 &lt;= x &lt; 10.0</span>
<span class="go">3.1800146073117523</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="go">5.148957571865031</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="go">7</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="go">26</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">choice</span><span class="p">([</span><span class="s1">&#39;win&#39;</span><span class="p">,</span> <span class="s1">&#39;lose&#39;</span><span class="p">,</span> <span class="s1">&#39;draw&#39;</span><span class="p">])</span> <span class="c1"># Single random element from a sequence</span>
<span class="go">&#39;draw&#39;</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">deck</span> <span class="o">=</span> <span class="s1">&#39;ace two three four&#39;</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="gp">&gt;&gt;&gt; </span><span class="n">deck</span>
<span class="go">[&#39;four&#39;, &#39;two&#39;, &#39;ace&#39;, &#39;three&#39;]</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="go">[40, 10, 50, 30]</span>
</pre></div>
</div>
<p>模拟:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="c1"># Six roulette wheel spins (weighted sampling with replacement)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">choices</span><span class="p">([</span><span class="s1">&#39;red&#39;</span><span class="p">,</span> <span class="s1">&#39;black&#39;</span><span class="p">,</span> <span class="s1">&#39;green&#39;</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>
<span class="go">[&#39;red&#39;, &#39;green&#39;, &#39;black&#39;, &#39;black&#39;, &#39;red&#39;, &#39;black&#39;]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c1"># Deal 20 cards without replacement from a deck of 52 playing cards</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c1"># and determine the proportion of cards with a ten-value</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c1"># (a ten, jack, queen, or king).</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">deck</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">Counter</span><span class="p">(</span><span class="n">tens</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span> <span class="n">low_cards</span><span class="o">=</span><span class="mi">36</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seen</span> <span class="o">=</span> <span class="n">sample</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">deck</span><span class="o">.</span><span class="n">elements</span><span class="p">()),</span> <span class="n">k</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">seen</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="s1">&#39;tens&#39;</span><span class="p">)</span> <span class="o">/</span> <span class="mi">20</span>
<span class="go">0.15</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c1"># Estimate the probability of getting 5 or more heads from 7 spins</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c1"># of a biased coin that settles on heads 60% of the time.</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">trial</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">return</span> <span class="n">choices</span><span class="p">(</span><span class="s1">&#39;HT&#39;</span><span class="p">,</span> <span class="n">cum_weights</span><span class="o">=</span><span class="p">(</span><span class="mf">0.60</span><span class="p">,</span> <span class="mf">1.00</span><span class="p">),</span> <span class="n">k</span><span class="o">=</span><span class="mi">7</span><span class="p">)</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="s1">&#39;H&#39;</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">5</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="go">0.4169</span>
<span class="gp">&gt;&gt;&gt; </span><span class="c1"># Probability of the median of 5 samples being in middle two quartiles</span>
<span class="gp">&gt;&gt;&gt; </span><span class="k">def</span> <span class="nf">trial</span><span class="p">():</span>
<span class="gp">... </span> <span class="k">return</span> <span class="mi">2_500</span> <span class="o">&lt;=</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">&lt;</span> <span class="mi">7_500</span>
<span class="gp">...</span>
<span class="gp">&gt;&gt;&gt; </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>
<span class="go">0.7958</span>
</pre></div>
</div>
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Bootstrapping_(statistics)">statistical bootstrapping</a> 的示例，使用重新采样和替换来估计一个样本的均值的置信区间:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm</span>
<span class="kn">from</span> <span class="nn">statistics</span> <span class="kn">import</span> <span class="n">fmean</span> <span class="k">as</span> <span class="n">mean</span>
<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">choices</span>
<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>
<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>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;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 &#39;</span>
<span class="sa">f</span><span class="s1">&#39;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">&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>使用 <a class="reference external" href="https://en.wikipedia.org/wiki/Resampling_(statistics)#Permutation_tests">重新采样排列测试</a> 来确定统计学显著性或者使用 <a class="reference external" href="https://en.wikipedia.org/wiki/P-value">p-值</a> 来观察药物与安慰剂的作用之间差异的示例:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Example from &quot;Statistics is Easy&quot; by Dennis Shasha and Manda Wilson</span>
<span class="kn">from</span> <span class="nn">statistics</span> <span class="kn">import</span> <span class="n">fmean</span> <span class="k">as</span> <span class="n">mean</span>
<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">shuffle</span>
<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>
<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>
<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>
<span class="n">n</span> <span class="o">=</span> <span class="mi">10_000</span>
<span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">combined</span> <span class="o">=</span> <span class="n">drug</span> <span class="o">+</span> <span class="n">placebo</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>
<span class="n">shuffle</span><span class="p">(</span><span class="n">combined</span><span class="p">)</span>
<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>
<span class="n">count</span> <span class="o">+=</span> <span class="p">(</span><span class="n">new_diff</span> <span class="o">&gt;=</span> <span class="n">observed_diff</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;</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&#39;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;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">.&#39;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;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&#39;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;hypothesis that there is no difference between the drug and the placebo.&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>多服务器队列的到达时间和服务交付模拟:</p>
<div class="highlight-python3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">heapq</span> <span class="kn">import</span> <span class="n">heappush</span><span class="p">,</span> <span class="n">heappop</span>
<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">expovariate</span><span class="p">,</span> <span class="n">gauss</span>
<span class="kn">from</span> <span class="nn">statistics</span> <span class="kn">import</span> <span class="n">mean</span><span class="p">,</span> <span class="n">median</span><span class="p">,</span> <span class="n">stdev</span>
<span class="n">average_arrival_interval</span> <span class="o">=</span> <span class="mf">5.6</span>
<span class="n">average_service_time</span> <span class="o">=</span> <span class="mf">15.0</span>
<span class="n">stdev_service_time</span> <span class="o">=</span> <span class="mf">3.5</span>
<span class="n">num_servers</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">waits</span> <span class="o">=</span> <span class="p">[]</span>
<span class="n">arrival_time</span> <span class="o">=</span> <span class="mf">0.0</span>
<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>
<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_000</span><span class="p">):</span>
<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>
<span class="n">next_server_available</span> <span class="o">=</span> <span class="n">heappop</span><span class="p">(</span><span class="n">servers</span><span class="p">)</span>
<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>
<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>
<span class="n">service_duration</span> <span class="o">=</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>
<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>
<span class="n">heappush</span><span class="p">(</span><span class="n">servers</span><span class="p">,</span> <span class="n">service_completed</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;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">. Stdev wait: </span><span class="si">{</span><span class="n">stdev</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">.&#39;</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Median wait: </span><span class="si">{</span><span class="n">median</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">.&#39;</span><span class="p">)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">参见</p>
<p><a class="reference external" href="https://www.youtube.com/watch?v=Iq9DzN6mvYA">Statistics for Hackers</a> <a class="reference external" href="https://us.pycon.org/2016/speaker/profile/295/">Jake Vanderplas</a> 撰写的视频教程，使用一些基本概念进行统计分析，包括模拟、抽样、改组和交叉验证。</p>
<p><a class="reference external" href="http://nbviewer.jupyter.org/url/norvig.com/ipython/Economics.ipynb">Economics Simulation</a> <a class="reference external" href="http://norvig.com/bio.html">Peter Norvig</a> 编写的市场模拟，显示了该模块提供的许多工具和分布的有效使用（高斯、均匀、样本、beta变量、选择、三角和随机范围等）。</p>
<p><a class="reference external" href="http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb">A Concrete Introduction to Probability (using Python)</a> <a class="reference external" href="http://norvig.com/bio.html">Peter Norvig</a> 撰写的教程，涵盖了概率论基础知识，如何编写模拟，以及如何使用 Python 进行数据分析。</p>
</div>
</section>
</section>
</div>
</div>
</div>
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
<div class="sphinxsidebarwrapper">
<h3><a href="../contents.html">目录</a></h3>
<ul>
<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">random</span></code> --- 生成伪随机数</a><ul>
<li><a class="reference internal" href="#bookkeeping-functions">簿记功能</a></li>
<li><a class="reference internal" href="#functions-for-integers">整数用函数</a></li>
<li><a class="reference internal" href="#functions-for-sequences">序列用函数</a></li>
<li><a class="reference internal" href="#real-valued-distributions">实值分布</a></li>
<li><a class="reference internal" href="#alternative-generator">替代生成器</a></li>
<li><a class="reference internal" href="#notes-on-reproducibility">关于再现性的说明</a></li>
<li><a class="reference internal" href="#examples-and-recipes">例子和配方</a></li>
</ul>
</li>
</ul>
<h4>上一个主题</h4>
<p class="topless"><a href="fractions.html"
title="上一章"><code class="xref py py-mod docutils literal notranslate"><span class="pre">fractions</span></code> --- 分数</a></p>
<h4>下一个主题</h4>
<p class="topless"><a href="statistics.html"
title="下一章"><code class="xref py py-mod docutils literal notranslate"><span class="pre">statistics</span></code> --- 数学统计函数</a></p>
<div role="note" aria-label="source link">
<h3>本页</h3>
<ul class="this-page-menu">
<li><a href="../bugs.html">报告 Bug</a></li>
<li>
<a href="https://github.com/python/cpython/blob/3.8/Doc/library/random.rst"
rel="nofollow">显示源代码
</a>
</li>
</ul>
</div>
</div>
</div>
<div class="clearer"></div>
</div>
<div class="related" role="navigation" aria-label="related navigation">
<h3>导航</h3>
<ul>
<li class="right" style="margin-right: 10px">
<a href="../genindex.html" title="总目录"
>索引</a></li>
<li class="right" >
<a href="../py-modindex.html" title="Python 模块索引"
>模块</a> |</li>
<li class="right" >
<a href="statistics.html" title="statistics --- 数学统计函数"
>下一页</a> |</li>
<li class="right" >
<a href="fractions.html" title="fractions --- 分数"
>上一页</a> |</li>
<li><img src="../_static/py.svg" alt="python logo" style="vertical-align: middle; margin-top: -1px"/></li>
<li><a href="https://www.python.org/">Python</a> &#187;</li>
<li class="switchers">
<div class="language_switcher_placeholder"></div>
<div class="version_switcher_placeholder"></div>
</li>
<li>
</li>
<li id="cpython-language-and-version">
<a href="../index.html">3.8.20 Documentation</a> &#187;
</li>
<li class="nav-item nav-item-1"><a href="index.html" >Python 标准库</a> &#187;</li>
<li class="nav-item nav-item-2"><a href="numeric.html" >数字和数学模块</a> &#187;</li>
<li class="right">
<div class="inline-search" role="search">
<form class="inline-search" action="../search.html" method="get">
<input placeholder="快速搜索" aria-label="快速搜索" type="text" name="q" />
<input type="submit" value="转向" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
|
</li>
</ul>
</div>
<div class="footer">
&copy; <a href="../copyright.html">版权所有</a> 2001-2024, Python Software Foundation.
<br />
This page is licensed under the Python Software Foundation License Version 2.
<br />
Examples, recipes, and other code in the documentation are additionally licensed under the Zero Clause BSD License.
<br />
<br />
The Python Software Foundation is a non-profit corporation.
<a href="https://www.python.org/psf/donations/">Please donate.</a>
<br />
<br />
最后更新于 12月 09, 2024.
<a href="https://docs.python.org/3/bugs.html">Found a bug</a>?
<br />
Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 2.4.4.
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink