260 lines
15 KiB
HTML
260 lines
15 KiB
HTML
<!DOCTYPE html>
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<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
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<head><meta http-equiv="x-ua-compatible" content="ie=edge">
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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<title>std::gamma_distribution</title>
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<link rel="stylesheet" href="ext.css" />
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<link rel="stylesheet" href="site_modules.css" />
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</head>
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<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_random_gamma_distribution skin-cppreference2 action-view cpp-navbar">
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<div id="cpp-content-base">
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<div id="content"><a id="top"></a>
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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>gamma_distribution</h1>
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<div id="bodyContent">
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<div id="contentSub"><span class="subpages">< <a href="cpp.html">cpp</a>‎ | <a href="cpp-numeric.html">numeric</a>‎ | <a href="cpp-numeric-random.html">random</a></span></div>
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<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
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<table class="t-dcl-begin">
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<tbody>
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<tr class="t-dsc-header">
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<td>
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<div>定义于头文件 <code><a href="cpp-header-random.html"><random></a></code></div>
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</td>
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<td></td>
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<td></td>
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</tr>
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<tr class="t-dcl t-since-cxx11">
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<td>
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1"><</span> <span class="kw1">class</span> RealType <span class="sy1">=</span> <span class="kw4">double</span> <span class="sy1">></span><br />
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<span class="kw1">class</span> gamma_distribution<span class="sy4">;</span></span></div>
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</td>
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<td class="t-dcl-nopad"></td>
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<td><span class="t-mark-rev t-since-cxx11">(C++11 起)</span></td>
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</tr>
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<tr class="t-dcl-sep">
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<td></td>
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<td></td>
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<td></td>
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</tr>
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</tbody>
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</table>
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<p>产生随机正浮点数 <span class="texhtml" style="white-space: nowrap;">x</span> ，分布服从概率密度函数：</p>
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<dl>
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<dd><span class="mjax" style="display:none">\(\mathsf{p}(x\mid\alpha,\beta) = \frac{e^{-x/\beta} }{\beta^\alpha\cdot\Gamma(\alpha)}\cdot x^{\alpha-1} \)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">P(x|α,β) = <span class="t-mfrac"></span></span>
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<table>
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<tr>
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<td>e<span class="t-su">-x/β<br /></span></td>
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</tr>
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<tr>
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<td>β<span class="t-su">α<br /></span> · Γ(α)</td>
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</tr>
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</table>
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· x<span class="t-su">α-1<br /></span></dd>
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</dl>
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<p>其中 <span class="texhtml" style="white-space: nowrap;">α</span> 被称为<i>形状</i>参数而 <span class="texhtml" style="white-space: nowrap;">β</span> 被称为<i>尺度</i>参数。形状参数有时以字母 <span class="texhtml" style="white-space: nowrap;">k</span> 表示，而尺度参数有时以字母 <span class="texhtml" style="white-space: nowrap;">θ</span> 表示。</p>
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<p>对于浮点 <span class="texhtml" style="white-space: nowrap;">α</span> ，获得的值是 <span class="texhtml" style="white-space: nowrap;">α</span> 个独立指数分布的随机变量的和，每个的平均值均为 <span class="texhtml" style="white-space: nowrap;">β</span> 。</p>
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<p><code>std::gamma_distribution</code> 满足<a href="cpp-named_req-RandomNumberDistribution.html"><span style="font-style:italic">随机数分布</span> <span style="font-family: Georgia, 'DejaVu Serif', serif; font-style:italic">(RandomNumberDistribution)</span></a> 。</p>
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<h3><span class="mw-headline" id=".E6.A8.A1.E6.9D.BF.E5.BD.A2.E5.8F.82">模板形参</span></h3>
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<table class="t-par-begin">
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<tr class="t-par">
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<td>RealType</td>
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<td>-</td>
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<td>生成器所生成的结果类型。若它不是 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> 或 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 之一则效果未定义。</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E7.B1.BB.E5.9E.8B">成员类型</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc-hitem">
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<td>成员类型</td>
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<td>定义</td>
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</tr>
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<tr class="t-dsc">
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<td><code>result_type</code></td>
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<td><span class="t-c"><span class="mw-geshi cpp source-cpp">RealType</span></span></td>
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</tr>
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<tr class="t-dsc">
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<td><code>param_type</code><span class="t-mark-rev t-since-cxx11">(C++11)</span></td>
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<td>参数集的类型，见<a href="cpp-named_req-RandomNumberDistribution.html"><span style="font-style:italic">随机数分布</span> <span style="font-family: Georgia, 'DejaVu Serif', serif; font-style:italic">(RandomNumberDistribution)</span></a> 。</td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">成员函数</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div t-dsc-member-nobold-div">
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<div><a href="cpp-numeric-random-gamma_distribution-gamma_distribution.html"><span class="t-lines"><span>(构造函数)</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>构造新分布<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-reset.html"><span class="t-lines"><span>reset</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>重置分布的内部状态<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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<tr>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E7.94.9F.E6.88.90">生成</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-operator().html"><span class="t-lines"><span>operator()</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>生成分布中的下个随机数<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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<tr>
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<td colspan="2">
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<h5><span class="mw-headline" id=".E7.89.B9.E5.BE.81">特征</span></h5>
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</td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-params.html"><span class="t-lines"><span>alpha</span><span>beta</span></span></a></div>
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</div>
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</td>
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<td>返回分布参数<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-param.html"><span class="t-lines"><span>param</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>获取或设置随机参数对象<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-min.html"><span class="t-lines"><span>min</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>返回最小的潜在生成值<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-max.html"><span class="t-lines"><span>max</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>返回最大的潜在生成值<br />
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<span class="t-mark">(公开成员函数)</span></td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E9.9D.9E.E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">非成员函数</span></h3>
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<table class="t-dsc-begin">
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-operator_cmp.html"><span class="t-lines"><span>operator==</span><span>operator!=</span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span><span><span class="t-mark-rev t-since-cxx11">(C++11)</span><span class="t-mark-rev t-until-cxx20">(C++20 中移除)</span></span></span></div>
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</div>
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</td>
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<td>比较两个分布对象<br />
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<span class="t-mark">(函数)</span></td>
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</tr>
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<tr class="t-dsc">
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<td>
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<div class="t-dsc-member-div">
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<div><a href="cpp-numeric-random-gamma_distribution-operator_ltltgtgt.html"><span class="t-lines"><span>operator<<</span><span>operator>></span></span></a></div>
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<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
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</div>
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</td>
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<td>执行伪随机数分布的流输入和输出<br />
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<span class="t-mark">(函数模板)</span></td>
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</tr>
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</table>
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<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
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<div class="t-example">
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<div class="t-example-live-link"></div>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="cpp source-cpp">
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<pre class="de1"><span class="co2">#include <iostream></span>
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<span class="co2">#include <iomanip></span>
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<span class="co2">#include <string></span>
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<span class="co2">#include <map></span>
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<span class="co2">#include <random></span>
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<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span>
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<span class="br0">{</span>
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<a href="cpp-numeric-random-random_device.html"><span class="kw1486">std::<span class="me2">random_device</span></span></a> rd<span class="sy4">;</span>
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<a href="cpp-numeric-random-mersenne_twister_engine.html"><span class="kw1489">std::<span class="me2">mt19937</span></span></a> gen<span class="br0">(</span>rd<span class="br0">(</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
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<span class="co1">// alpha=1 ， beta=2 的 gamma 分布近似于指数分布。</span>
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std<span class="sy4">::</span><span class="me2">gamma_distribution</span><span class="sy1"><></span> d<span class="br0">(</span><span class="nu0">1</span>,<span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span>
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<a href="cpp-container-map.html"><span class="kw1281">std::<span class="me2">map</span></span></a><span class="sy1"><</span><span class="kw4">int</span>, <span class="kw4">int</span><span class="sy1">></span> hist<span class="sy4">;</span>
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<span class="kw1">for</span><span class="br0">(</span><span class="kw4">int</span> n<span class="sy1">=</span><span class="nu0">0</span><span class="sy4">;</span> n<span class="sy1"><</span><span class="nu0">10000</span><span class="sy4">;</span> <span class="sy2">++</span>n<span class="br0">)</span> <span class="br0">{</span>
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<span class="sy2">++</span>hist<span class="br0">[</span><span class="nu0">2</span><span class="sy2">*</span>d<span class="br0">(</span>gen<span class="br0">)</span><span class="br0">]</span><span class="sy4">;</span>
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<span class="br0">}</span>
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<span class="kw1">for</span><span class="br0">(</span><span class="kw4">auto</span> p <span class="sy4">:</span> hist<span class="br0">)</span> <span class="br0">{</span>
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<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-fixed.html"><span class="kw1783">std::<span class="me2">fixed</span></span></a> <span class="sy1"><<</span> <a href="cpp-io-manip-setprecision.html"><span class="kw1795">std::<span class="me2">setprecision</span></span></a><span class="br0">(</span><span class="nu0">1</span><span class="br0">)</span>
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<span class="sy1"><<</span> p.<span class="me1">first</span><span class="sy2">/</span><span class="nu16">2.0</span> <span class="sy1"><<</span> <span class="st0">'-'</span> <span class="sy1"><<</span> <span class="br0">(</span>p.<span class="me1">first</span><span class="sy2">+</span><span class="nu0">1</span><span class="br0">)</span><span class="sy2">/</span><span class="nu16">2.0</span> <span class="sy1"><<</span>
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<span class="st0">' '</span> <span class="sy1"><<</span> <a href="cpp-string-basic_string.html"><span class="kw1230">std::<span class="me2">string</span></span></a><span class="br0">(</span>p.<span class="me1">second</span><span class="sy2">/</span><span class="nu0">200</span>, <span class="st0">'*'</span><span class="br0">)</span> <span class="sy1"><<</span> <span class="st0">'<span class="es1">\n</span>'</span><span class="sy4">;</span>
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<span class="br0">}</span>
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<span class="br0">}</span></pre></div>
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</div>
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<p>可能的输出：</p>
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<div dir="ltr" class="mw-geshi" style="text-align: left;">
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<div class="text source-text">
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<pre class="de1">0.0-0.5 **********
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0.5-1.0 ********
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1.0-1.5 ******
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1.5-2.0 *****
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2.0-2.5 ****
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2.5-3.0 ***
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3.0-3.5 **
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3.5-4.0 *
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4.0-4.5 *
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4.5-5.0 *
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5.0-5.5 *
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5.5-6.0
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6.0-6.5
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6.5-7.0
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7.0-7.5
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7.5-8.0
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8.5-9.0
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9.5-10.0
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10.0-10.5
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10.5-11.0
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11.0-11.5
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11.5-12.0
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12.5-13.0
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18.0-18.5
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18.5-19.0</pre></div>
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</div>
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</div>
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<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">外部链接</span></h3>
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<p><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/GammaDistribution.html">Weisstein, Eric W. “ Γ 分布。”</a>来自 MathWorld--A Wolfram Web Resource 。</p>
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</div>
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<div class="visualClear"></div>
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</body>
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</html>
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