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<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>chi_squared_distribution</h1>
<div id="bodyContent">
<div id="contentSub"><span class="subpages">&lt; <a href="cpp.html">cpp</a>&lrm; | <a href="cpp-numeric.html">numeric</a>&lrm; | <a href="cpp-numeric-random.html">random</a></span></div>
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<table class="t-dcl-begin">
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<div>&#23450;&#20041;&#20110;&#22836;&#25991;&#20214; <code><a href="cpp-header-random.html">&lt;random&gt;</a></code></div>
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<td></td>
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<tr class="t-dcl t-since-cxx11">
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<div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1">&lt;</span> <span class="kw1">class</span> RealType <span class="sy1">=</span> <span class="kw4">double</span> <span class="sy1">&gt;</span><br />
<span class="kw1">class</span> chi_squared_distribution<span class="sy4">;</span></span></div>
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<td class="t-dcl-nopad"></td>
<td><span class="t-mark-rev t-since-cxx11">(C++11 &#36215;)</span></td>
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<p><code>chi_squared_distribution</code> &#20135;&#29983;&#38543;&#26426;&#25968; <span class="mjax" style="display:none">\(\small x&gt;0\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">x&gt;0</span> &#65292;&#26381;&#20174; <a href="https://en.wikipedia.org/wiki/Chi-squared_distribution" class="extiw" title="enwiki:Chi-squared distribution">&chi;<sup>2</sup> &#20998;&#24067;</a>&#65306;</p>
<dl>
<dd><span class="mjax" style="display:none">\({\small f(x;n) = }\frac{x^{(n/2)-1}\exp{(-x/2)} }{\Gamma{(n/2)}2^{n/2} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">f(x;n) = <span class="t-mfrac"></span></span>
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<td>x<span class="t-su">(n/2)-1<br /></span> <i>e</i><sup>-x/2</sup></td>
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<td>&Gamma;(n/2) 2<span class="t-su">n/2<br /></span></td>
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</dd>
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<p><span class="mjax" style="display:none">\(\small\Gamma\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">&Gamma;</span> &#20026; <a href="https://en.wikipedia.org/wiki/Gamma_function" class="extiw" title="enwiki:Gamma function">&Gamma; &#20989;&#25968;</a>&#65288;&#21442;&#38405; <span class="t-lc"><a href="cpp-numeric-math-tgamma.html">std::tgamma</a></span> &#65289;&#32780; <span class="mjax" style="display:none">\(\small n\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">n</span> &#20026;<a href="https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)" class="extiw" title="enwiki:Degrees of freedom (statistics)">&#33258;&#30001;&#24230;</a>&#65288;&#40664;&#35748;&#20026; 1 &#65289;&#12290;</p>
<p><code>std::chi_squared_distribution</code> &#28385;&#36275;<a href="cpp-named_req-RandomNumberDistribution.html"><span style="font-style:italic">&#38543;&#26426;&#25968;&#20998;&#24067;</span> <span style="font-family: Georgia, &#39;DejaVu Serif&#39;, serif; font-style:italic">(RandomNumberDistribution)</span></a> &#30340;&#25152;&#26377;&#35201;&#27714;&#12290;</p>
<h3><span class="mw-headline" id=".E6.A8.A1.E6.9D.BF.E5.BD.A2.E5.8F.82">&#27169;&#26495;&#24418;&#21442;</span></h3>
<table class="t-par-begin">
<tr class="t-par">
<td>RealType</td>
<td>-</td>
<td>&#29983;&#25104;&#22120;&#25152;&#29983;&#25104;&#30340;&#32467;&#26524;&#31867;&#22411;&#12290;&#33509;&#23427;&#19981;&#26159; <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">float</span></span></span> &#12289; <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">double</span></span></span> &#25110; <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">long</span> <span class="kw4">double</span></span></span> &#20043;&#19968;&#21017;&#25928;&#26524;&#26410;&#23450;&#20041;&#12290;</td>
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<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E7.B1.BB.E5.9E.8B">&#25104;&#21592;&#31867;&#22411;</span></h3>
<table class="t-dsc-begin">
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<td>&#25104;&#21592;&#31867;&#22411;</td>
<td>&#23450;&#20041;</td>
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<tr class="t-dsc">
<td><code>result_type</code><span class="t-mark-rev t-since-cxx11">(C++11)</span></td>
<td><span class="t-c"><span class="mw-geshi cpp source-cpp">RealType</span></span></td>
</tr>
<tr class="t-dsc">
<td><code>param_type</code><span class="t-mark-rev t-since-cxx11">(C++11)</span></td>
<td>&#21442;&#25968;&#38598;&#30340;&#31867;&#22411;&#65292;&#35265;<a href="cpp-named_req-RandomNumberDistribution.html"><span style="font-style:italic">&#38543;&#26426;&#25968;&#20998;&#24067;</span> <span style="font-family: Georgia, &#39;DejaVu Serif&#39;, serif; font-style:italic">(RandomNumberDistribution)</span></a> &#12290;</td>
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<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">&#25104;&#21592;&#20989;&#25968;</span></h3>
<table class="t-dsc-begin">
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<td>
<div class="t-dsc-member-div t-dsc-member-nobold-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-chi_squared_distribution.html"><span class="t-lines"><span>(&#26500;&#36896;&#20989;&#25968;)</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#26500;&#36896;&#26032;&#20998;&#24067;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-reset.html"><span class="t-lines"><span>reset</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#37325;&#32622;&#20998;&#24067;&#30340;&#20869;&#37096;&#29366;&#24577;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
<tr>
<td colspan="2">
<h5><span class="mw-headline" id=".E7.94.9F.E6.88.90">&#29983;&#25104;</span></h5>
</td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-operator().html"><span class="t-lines"><span>operator()</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#29983;&#25104;&#20998;&#24067;&#20013;&#30340;&#19979;&#20010;&#38543;&#26426;&#25968;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
<tr>
<td colspan="2">
<h5><span class="mw-headline" id=".E7.89.B9.E5.BE.81">&#29305;&#24449;</span></h5>
</td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-n.html"><span class="t-lines"><span>n</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#36820;&#22238;&#33258;&#30001;&#24230;&#65288; <span class="mjax" style="display:none">\(\small n\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">n</span> &#65289;&#20998;&#24067;&#21442;&#25968;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-param.html"><span class="t-lines"><span>param</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#33719;&#21462;&#25110;&#35774;&#32622;&#38543;&#26426;&#21442;&#25968;&#23545;&#35937;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-min.html"><span class="t-lines"><span>min</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#36820;&#22238;&#26368;&#23567;&#30340;&#28508;&#22312;&#29983;&#25104;&#20540;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-max.html"><span class="t-lines"><span>max</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#36820;&#22238;&#26368;&#22823;&#30340;&#28508;&#22312;&#29983;&#25104;&#20540;<br />
<span class="t-mark">(&#20844;&#24320;&#25104;&#21592;&#20989;&#25968;)</span></td>
</tr>
</table>
<h3><span class="mw-headline" id=".E9.9D.9E.E6.88.90.E5.91.98.E5.87.BD.E6.95.B0">&#38750;&#25104;&#21592;&#20989;&#25968;</span></h3>
<table class="t-dsc-begin">
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-operator_cmp.html"><span class="t-lines"><span>operator==</span><span>operator!=</span></span></a></div>
<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 &#20013;&#31227;&#38500;)</span></span></span></div>
</div>
</td>
<td>&#27604;&#36739;&#20004;&#20010;&#20998;&#24067;&#23545;&#35937;<br />
<span class="t-mark">(&#20989;&#25968;)</span></td>
</tr>
<tr class="t-dsc">
<td>
<div class="t-dsc-member-div">
<div><a href="cpp-numeric-random-chi_squared_distribution-operator_ltltgtgt.html"><span class="t-lines"><span>operator&lt;&lt;</span><span>operator&gt;&gt;</span></span></a></div>
<div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div>
</div>
</td>
<td>&#25191;&#34892;&#20266;&#38543;&#26426;&#25968;&#20998;&#24067;&#30340;&#27969;&#36755;&#20837;&#21644;&#36755;&#20986;<br />
<span class="t-mark">(&#20989;&#25968;&#27169;&#26495;)</span></td>
</tr>
</table>
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">&#31034;&#20363;</span></h3>
<div class="t-example">
<div class="t-example-live-link"></div>
<div dir="ltr" class="mw-geshi" style="text-align: left;">
<div class="cpp source-cpp">
<pre class="de1"><span class="co2">#include &lt;algorithm&gt;</span>
<span class="co2">#include &lt;cmath&gt;</span>
<span class="co2">#include &lt;iomanip&gt;</span>
<span class="co2">#include &lt;iostream&gt;</span>
<span class="co2">#include &lt;map&gt;</span>
<span class="co2">#include &lt;random&gt;</span>
<span class="co2">#include &lt;vector&gt;</span>
<span class="kw1">template</span> <span class="sy1">&lt;</span><span class="kw4">int</span> Height <span class="sy1">=</span> <span class="nu0">5</span>, <span class="kw4">int</span> BarWidth <span class="sy1">=</span> <span class="nu0">1</span>, <span class="kw4">int</span> Padding <span class="sy1">=</span> <span class="nu0">1</span>, <span class="kw4">int</span> Offset <span class="sy1">=</span> <span class="nu0">0</span>,
<span class="kw4">bool</span> DrawMinMax <span class="sy1">=</span> <span class="kw2">true</span>, <span class="kw1">class</span> Sample<span class="sy1">&gt;</span>
<span class="kw4">void</span> draw_vbars<span class="br0">(</span>Sample <span class="kw4">const</span><span class="sy3">&amp;</span> s<span class="br0">)</span> <span class="br0">{</span>
static_assert<span class="br0">(</span><span class="br0">(</span>Height <span class="sy1">&gt;</span> <span class="nu0">0</span><span class="br0">)</span> <span class="sy3">&amp;&amp;</span> <span class="br0">(</span>BarWidth <span class="sy1">&gt;</span> <span class="nu0">0</span><span class="br0">)</span> <span class="sy3">&amp;&amp;</span> <span class="br0">(</span>Padding <span class="sy1">&gt;=</span> <span class="nu0">0</span><span class="br0">)</span> <span class="sy3">&amp;&amp;</span> <span class="br0">(</span>Offset <span class="sy1">&gt;=</span> <span class="nu0">0</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">auto</span> cout_n <span class="sy1">=</span> <span class="br0">[</span><span class="br0">]</span><span class="br0">(</span><span class="kw4">auto</span> <span class="kw4">const</span><span class="sy3">&amp;</span> v, <span class="kw4">int</span> n<span class="br0">)</span> <span class="br0">{</span> <span class="kw1">while</span> <span class="br0">(</span>n<span class="sy2">--</span> <span class="sy1">&gt;</span> <span class="nu0">0</span><span class="br0">)</span> <a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> v<span class="sy4">;</span> <span class="br0">}</span><span class="sy4">;</span>
<span class="kw4">const</span> <span class="kw4">auto</span> <span class="br0">[</span>min, max<span class="br0">]</span> <span class="sy1">=</span> <a href="cpp-algorithm-minmax_element.html"><span class="kw1644">std::<span class="me2">minmax_element</span></span></a><span class="br0">(</span><a href="cpp-iterator-begin.html"><span class="kw677">std::<span class="me2">cbegin</span></span></a><span class="br0">(</span>s<span class="br0">)</span>, <a href="cpp-iterator-end.html"><span class="kw681">std::<span class="me2">cend</span></span></a><span class="br0">(</span>s<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
<a href="cpp-container-vector.html"><span class="kw1269">std::<span class="me2">vector</span></span></a><span class="sy1">&lt;</span><a href="cpp-numeric-math-div.html"><span class="kw1307">std::<span class="me2">div_t</span></span></a><span class="sy1">&gt;</span> qr<span class="sy4">;</span>
<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">float</span> e <span class="sy4">:</span> s<span class="br0">)</span> <span class="br0">{</span>
qr.<span class="me1">push_back</span><span class="br0">(</span><a href="cpp-numeric-math-div.html"><span class="kw1303">std::<span class="me2">div</span></span></a><span class="br0">(</span>std<span class="sy4">::</span><span class="me2">lerp</span><span class="br0">(</span><span class="nu0">0</span>.<span class="me1">f</span>, Height<span class="sy2">*</span><span class="nu0">8</span>, <span class="br0">(</span>e <span class="sy2">-</span> <span class="sy2">*</span>min<span class="br0">)</span><span class="sy2">/</span><span class="br0">(</span><span class="sy2">*</span>max <span class="sy2">-</span> <span class="sy2">*</span>min<span class="br0">)</span><span class="br0">)</span>, <span class="nu0">8</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span>
<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">auto</span> h<span class="br0">{</span>Height<span class="br0">}</span><span class="sy4">;</span> h<span class="sy2">--</span> <span class="sy1">&gt;</span> <span class="nu0">0</span> <span class="sy4">;</span><span class="br0">)</span> <span class="br0">{</span>
cout_n<span class="br0">(</span><span class="st0">&#39; &#39;</span>, Offset<span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">auto</span> <span class="br0">[</span>q, r<span class="br0">]</span> <span class="sy4">:</span> qr<span class="br0">)</span> <span class="br0">{</span>
<span class="kw4">char</span> d<span class="br0">[</span><span class="br0">]</span> <span class="sy1">=</span> <span class="st0">&quot;&#9608;&quot;</span><span class="sy4">;</span> <span class="co1">// == { 0xe2, 0x96, 0x88, 0 }</span>
q <span class="sy1">&lt;</span> h <span class="sy4">?</span> d<span class="br0">[</span><span class="nu0">0</span><span class="br0">]</span> <span class="sy1">=</span> <span class="st0">&#39; &#39;</span>, d<span class="br0">[</span><span class="nu0">1</span><span class="br0">]</span> <span class="sy1">=</span> <span class="st0">&#39;<span class="es5">\0</span>&#39;</span> <span class="sy4">:</span> q <span class="sy1">==</span> h <span class="sy4">?</span> d<span class="br0">[</span><span class="nu0">2</span><span class="br0">]</span> <span class="sy2">-</span><span class="sy1">=</span> <span class="br0">(</span><span class="nu0">7</span> <span class="sy2">-</span> r<span class="br0">)</span> <span class="sy4">:</span> <span class="nu0">0</span><span class="sy4">;</span>
cout_n<span class="br0">(</span>d, BarWidth<span class="br0">)</span><span class="sy4">;</span>
cout_n<span class="br0">(</span><span class="st0">&#39; &#39;</span>, Padding<span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span>
<span class="kw1">if</span> <span class="br0">(</span>DrawMinMax <span class="sy3">&amp;&amp;</span> Height <span class="sy1">&gt;</span> <span class="nu0">1</span><span class="br0">)</span>
h <span class="sy1">==</span> Height <span class="sy2">-</span> <span class="nu0">1</span> <span class="sy4">?</span> <a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;&#9516; &quot;</span> <span class="sy1">&lt;&lt;</span> <span class="sy2">*</span>max<span class="sy4">:</span>
h <span class="sy3">!</span><span class="sy1">=</span> <span class="nu0">0</span> <span class="sy4">?</span> <a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;&#9474;&quot;</span>
<span class="sy4">:</span> <a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;&#9524; &quot;</span> <span class="sy1">&lt;&lt;</span> <span class="sy2">*</span>min<span class="sy4">;</span>
cout_n<span class="br0">(</span><span class="st0">&#39;<span class="es1">\n</span>&#39;</span>, <span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span>
<span class="br0">}</span>
<span class="kw4">int</span> main<span class="br0">(</span><span class="br0">)</span> <span class="br0">{</span>
<a href="cpp-numeric-random-random_device.html"><span class="kw1486">std::<span class="me2">random_device</span></span></a> rd<span class="br0">{</span><span class="br0">}</span><span class="sy4">;</span>
<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>
<span class="kw4">auto</span> &chi;&sup2; <span class="sy1">=</span> <span class="br0">[</span><span class="sy3">&amp;</span>gen<span class="br0">]</span><span class="br0">(</span><span class="kw4">const</span> <span class="kw4">float</span> dof<span class="br0">)</span> <span class="br0">{</span>
std<span class="sy4">::</span><span class="me2">chi_squared_distribution</span><span class="sy1">&lt;</span><span class="kw4">float</span><span class="sy1">&gt;</span> d<span class="br0">{</span> dof <span class="coMULTI">/* n */</span> <span class="br0">}</span><span class="sy4">;</span>
<span class="kw4">const</span> <span class="kw4">int</span> norm <span class="sy1">=</span> <span class="nu0">1</span><span class="st0">&#39;00&#39;</span><span class="nu8">00</span><span class="sy4">;</span>
<span class="kw4">const</span> <span class="kw4">float</span> cutoff <span class="sy1">=</span> <span class="nu17">0.002f</span><span class="sy4">;</span>
<a href="cpp-container-map.html"><span class="kw1281">std::<span class="me2">map</span></span></a><span class="sy1">&lt;</span><span class="kw4">int</span>, <span class="kw4">int</span><span class="sy1">&gt;</span> hist<span class="br0">{</span><span class="br0">}</span><span class="sy4">;</span>
<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="sy3">!</span><span class="sy1">=</span>norm<span class="sy4">;</span> <span class="sy2">++</span>n<span class="br0">)</span> <span class="br0">{</span> <span class="sy2">++</span>hist<span class="br0">[</span><a href="cpp-numeric-math-round.html"><span class="kw1353">std::<span class="me2">round</span></span></a><span class="br0">(</span>d<span class="br0">(</span>gen<span class="br0">)</span><span class="br0">)</span><span class="br0">]</span><span class="sy4">;</span> <span class="br0">}</span>
<a href="cpp-container-vector.html"><span class="kw1269">std::<span class="me2">vector</span></span></a><span class="sy1">&lt;</span><span class="kw4">float</span><span class="sy1">&gt;</span> bars<span class="sy4">;</span>
<a href="cpp-container-vector.html"><span class="kw1269">std::<span class="me2">vector</span></span></a><span class="sy1">&lt;</span><span class="kw4">int</span><span class="sy1">&gt;</span> indices<span class="sy4">;</span>
<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">const</span> <span class="kw4">auto</span> <span class="br0">[</span>n, p<span class="br0">]</span> <span class="sy4">:</span> hist<span class="br0">)</span> <span class="br0">{</span>
<span class="kw1">if</span> <span class="br0">(</span><span class="kw4">float</span> x <span class="sy1">=</span> p <span class="sy2">*</span> <span class="br0">(</span><span class="nu16">1.0</span><span class="sy2">/</span>norm<span class="br0">)</span><span class="sy4">;</span> cutoff <span class="sy1">&lt;</span> x<span class="br0">)</span> <span class="br0">{</span>
bars.<span class="me1">push_back</span><span class="br0">(</span>x<span class="br0">)</span><span class="sy4">;</span>
indices.<span class="me1">push_back</span><span class="br0">(</span>n<span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span>
<span class="br0">}</span>
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;dof = &quot;</span> <span class="sy1">&lt;&lt;</span> dof <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;:<span class="es1">\n</span>&quot;</span><span class="sy4">;</span>
draw_vbars<span class="sy1">&lt;</span><span class="nu0">4</span>,<span class="nu0">3</span><span class="sy1">&gt;</span><span class="br0">(</span>bars<span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">int</span> n <span class="sy4">:</span> indices<span class="br0">)</span> <span class="br0">{</span> <a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;&quot;</span> <span class="sy1">&lt;&lt;</span> <a href="cpp-io-manip-setw.html"><span class="kw1796">std::<span class="me2">setw</span></span></a><span class="br0">(</span><span class="nu0">2</span><span class="br0">)</span> <span class="sy1">&lt;&lt;</span> n <span class="sy1">&lt;&lt;</span> <span class="st0">&quot; &quot;</span><span class="sy4">;</span> <span class="br0">}</span>
<a href="cpp-io-cout.html"><span class="kw1757">std::<span class="me2">cout</span></span></a> <span class="sy1">&lt;&lt;</span> <span class="st0">&quot;<span class="es1">\n</span><span class="es1">\n</span>&quot;</span><span class="sy4">;</span>
<span class="br0">}</span><span class="sy4">;</span>
<span class="kw1">for</span> <span class="br0">(</span><span class="kw4">float</span> dof <span class="sy4">:</span> <span class="br0">{</span><span class="nu0">1</span>.<span class="me1">f</span>, <span class="nu0">2</span>.<span class="me1">f</span>, <span class="nu0">3</span>.<span class="me1">f</span>, <span class="nu0">4</span>.<span class="me1">f</span>, <span class="nu0">6</span>.<span class="me1">f</span>, <span class="nu0">9</span>.<span class="me1">f</span><span class="br0">}</span><span class="br0">)</span> &chi;&sup2;<span class="br0">(</span>dof<span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span></pre></div>
</div>
<p>&#21487;&#33021;&#30340;&#36755;&#20986;&#65306;</p>
<div dir="ltr" class="mw-geshi" style="text-align: left;">
<div class="text source-text">
<pre class="de1">
dof = 1:
&#9608;&#9608;&#9608; &#9516; 0.5271
&#9608;&#9608;&#9608; &#9474;
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9474;
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9607;&#9607;&#9607; &#9603;&#9603;&#9603; &#9602;&#9602;&#9602; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9524; 0.003
0 1 2 3 4 5 6 7 8
dof = 2:
&#9608;&#9608;&#9608; &#9516; 0.3169
&#9606;&#9606;&#9606; &#9608;&#9608;&#9608; &#9603;&#9603;&#9603; &#9474;
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9604;&#9604;&#9604; &#9474;
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9607;&#9607;&#9607; &#9604;&#9604;&#9604; &#9603;&#9603;&#9603; &#9602;&#9602;&#9602; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9524; 0.004
0 1 2 3 4 5 6 7 8 9 10
dof = 3:
&#9608;&#9608;&#9608; &#9603;&#9603;&#9603; &#9516; 0.2439
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9604;&#9604;&#9604; &#9474;
&#9603;&#9603;&#9603; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9607;&#9607;&#9607; &#9601;&#9601;&#9601; &#9474;
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9606;&#9606;&#9606; &#9604;&#9604;&#9604; &#9603;&#9603;&#9603; &#9602;&#9602;&#9602; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9524; 0.0033
0 1 2 3 4 5 6 7 8 9 10 11 12
dof = 4:
&#9602;&#9602;&#9602; &#9608;&#9608;&#9608; &#9603;&#9603;&#9603; &#9516; 0.1864
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9602;&#9602;&#9602; &#9474;
&#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9605;&#9605;&#9605; &#9601;&#9601;&#9601; &#9474;
&#9605;&#9605;&#9605; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9606;&#9606;&#9606; &#9604;&#9604;&#9604; &#9603;&#9603;&#9603; &#9602;&#9602;&#9602; &#9602;&#9602;&#9602; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9524; 0.0026
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
dof = 6:
&#9605;&#9605;&#9605; &#9607;&#9607;&#9607; &#9608;&#9608;&#9608; &#9602;&#9602;&#9602; &#9516; 0.1351
&#9605;&#9605;&#9605; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9607;&#9607;&#9607; &#9601;&#9601;&#9601; &#9474;
&#9601;&#9601;&#9601; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9605;&#9605;&#9605; &#9602;&#9602;&#9602; &#9474;
&#9601;&#9601;&#9601; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9605;&#9605;&#9605; &#9604;&#9604;&#9604; &#9603;&#9603;&#9603; &#9602;&#9602;&#9602; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9524; 0.0031
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
dof = 9:
&#9605;&#9605;&#9605; &#9607;&#9607;&#9607; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9604;&#9604;&#9604; &#9602;&#9602;&#9602; &#9516; 0.1044
&#9603;&#9603;&#9603; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9605;&#9605;&#9605; &#9601;&#9601;&#9601; &#9474;
&#9604;&#9604;&#9604; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9606;&#9606;&#9606; &#9603;&#9603;&#9603; &#9474;
&#9604;&#9604;&#9604; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9608;&#9608;&#9608; &#9606;&#9606;&#9606; &#9604;&#9604;&#9604; &#9603;&#9603;&#9603; &#9602;&#9602;&#9602; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9601;&#9601;&#9601; &#9524; 0.0034
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22</pre></div>
</div>
</div>
<h3><span class="mw-headline" id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5">&#22806;&#37096;&#38142;&#25509;</span></h3>
<ul>
<li><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html">Weisstein, Eric W. &ldquo; &Chi;<sup>2</sup> &#20998;&#24067;&rdquo;</a>&#26469;&#33258; MathWorld--A Wolfram Web Resource &#12290;</li>
<li><a href="https://en.wikipedia.org/wiki/Chi-squared_distribution" class="extiw" title="enwiki:Chi-squared distribution">&chi;<sup>2</sup> &#20998;&#24067;</a>&#26469;&#33258;&#32500;&#22522;&#30334;&#31185;&#12290;</li>
</ul>
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