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<div class="title">std::normal_distribution< _RealType > Class Template Reference<div class="ingroups"><a class="el" href="a01476.html">Numerics</a> » <a class="el" href="a01494.html">Random Number Generation</a> » <a class="el" href="a01535.html">Random Number Distributions</a> » <a class="el" href="a01537.html">Normal Distributions</a></div></div> </div>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">struct  </td><td class="memItemRight" valign="bottom"><a class="el" href="a06315.html">param_type</a></td></tr>
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Public Types</h2></td></tr>
<tr class="memitem:ae45488abda3f5b20d944da2da5a70001"><td class="memItemLeft" align="right" valign="top">typedef _RealType </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a></td></tr>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a658ac956ac7ba2337b60388d188d09cf"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#a658ac956ac7ba2337b60388d188d09cf">normal_distribution</a> (<a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> __mean=<a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a>(0), <a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> __stddev=<a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a>(1))</td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>normal_distribution</b> (const <a class="el" href="a06315.html">param_type</a> &__p)</td></tr>
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template<typename _ForwardIterator , typename _UniformRandomNumberGenerator > </td></tr>
<tr class="memitem:a9a34eb16548d9b9c0ca550fc1978425a"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><b>__generate</b> (_ForwardIterator __f, _ForwardIterator __t, _UniformRandomNumberGenerator &__urng)</td></tr>
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template<typename _ForwardIterator , typename _UniformRandomNumberGenerator > </td></tr>
<tr class="memitem:a0acace466d66dc36f8b53bb5d9f6415b"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><b>__generate</b> (_ForwardIterator __f, _ForwardIterator __t, _UniformRandomNumberGenerator &__urng, const <a class="el" href="a06315.html">param_type</a> &__p)</td></tr>
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template<typename _UniformRandomNumberGenerator > </td></tr>
<tr class="memitem:aa5a06493b317be1649d3a60b028e5dad"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><b>__generate</b> (<a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> *__f, <a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> *__t, _UniformRandomNumberGenerator &__urng, const <a class="el" href="a06315.html">param_type</a> &__p)</td></tr>
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<tr class="memitem:ae433f04f988a93f6e835d7cf7fbbde31"><td class="memItemLeft" align="right" valign="top"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#ae433f04f988a93f6e835d7cf7fbbde31">max</a> () const</td></tr>
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<tr class="memitem:abcc6e9b8ff25f5d1e076cb5f51f42231"><td class="memItemLeft" align="right" valign="top">_RealType </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#abcc6e9b8ff25f5d1e076cb5f51f42231">mean</a> () const</td></tr>
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<tr class="memitem:aa79e79b65edcb6f45dda08b3efdff9e8"><td class="memItemLeft" align="right" valign="top"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#aa79e79b65edcb6f45dda08b3efdff9e8">min</a> () const</td></tr>
<tr class="separator:aa79e79b65edcb6f45dda08b3efdff9e8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae67f6ec56c5564a3521d734d90f35501"><td class="memTemplParams" colspan="2">template<typename _UniformRandomNumberGenerator > </td></tr>
<tr class="memitem:ae67f6ec56c5564a3521d734d90f35501"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a06311.html#ae67f6ec56c5564a3521d734d90f35501">operator()</a> (_UniformRandomNumberGenerator &__urng)</td></tr>
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<tr class="memitem:a159f2f44c19a01c99cb937297d03604c"><td class="memTemplParams" colspan="2">template<typename _UniformRandomNumberGenerator > </td></tr>
<tr class="memitem:a159f2f44c19a01c99cb937297d03604c"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a06311.html#a159f2f44c19a01c99cb937297d03604c">operator()</a> (_UniformRandomNumberGenerator &__urng, const <a class="el" href="a06315.html">param_type</a> &__p)</td></tr>
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<tr class="memitem:a9e150060b4fd9ea4fef8f07d8b249944"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#a9e150060b4fd9ea4fef8f07d8b249944">param</a> (const <a class="el" href="a06315.html">param_type</a> &__param)</td></tr>
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<tr class="memitem:a757217130ef7b0eb980500afc8bd865c"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#a757217130ef7b0eb980500afc8bd865c">reset</a> ()</td></tr>
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<tr class="memitem:a43aa93573bdffbacfde869b5a11bed31"><td class="memItemLeft" align="right" valign="top">_RealType </td><td class="memItemRight" valign="bottom"><a class="el" href="a06311.html#a43aa93573bdffbacfde869b5a11bed31">stddev</a> () const</td></tr>
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Friends</h2></td></tr>
<tr class="memitem:abdfecf8325ed9e856625871fee2c56a3"><td class="memTemplParams" colspan="2">template<typename _RealType1 , typename _CharT , typename _Traits > </td></tr>
<tr class="memitem:abdfecf8325ed9e856625871fee2c56a3"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a02463.html">std::basic_ostream</a>< _CharT, _Traits > & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a06311.html#abdfecf8325ed9e856625871fee2c56a3">operator<<</a> (<a class="el" href="a02463.html">std::basic_ostream</a>< _CharT, _Traits > &__os, const <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType1 > &__x)</td></tr>
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<tr class="memitem:afaafdb22ede1508109622f89f50e213d"><td class="memTemplParams" colspan="2">template<typename _RealType1 > </td></tr>
<tr class="memitem:afaafdb22ede1508109622f89f50e213d"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a06311.html#afaafdb22ede1508109622f89f50e213d">operator==</a> (const <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType1 > &__d1, const <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType1 > &__d2)</td></tr>
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<tr class="memitem:ac440bfeab944ac2efe370a05088ed47c"><td class="memTemplParams" colspan="2">template<typename _RealType1 , typename _CharT , typename _Traits > </td></tr>
<tr class="memitem:ac440bfeab944ac2efe370a05088ed47c"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="a02459.html">std::basic_istream</a>< _CharT, _Traits > & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a06311.html#ac440bfeab944ac2efe370a05088ed47c">operator>></a> (<a class="el" href="a02459.html">std::basic_istream</a>< _CharT, _Traits > &__is, <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType1 > &__x)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template<typename _RealType = double><br />
class std::normal_distribution< _RealType ></h3>
<p>A normal continuous distribution for random numbers. </p>
<p>The formula for the normal probability density function is </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ p(x|\mu,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}} e^{- \frac{{x - \mu}^ {2}}{2 \sigma ^ {2}} } \]" src="form_5.png"/>
</p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l01925">1925</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
</div><h2 class="groupheader">Member Typedef Documentation</h2>
<a id="ae45488abda3f5b20d944da2da5a70001"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae45488abda3f5b20d944da2da5a70001">◆ </a></span>result_type</h2>
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template<typename _RealType = double> </div>
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<td class="memname">typedef _RealType <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType >::<a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a></td>
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<p>The type of the range of the distribution. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l01928">1928</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<h2 class="groupheader">Constructor & Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a658ac956ac7ba2337b60388d188d09cf">◆ </a></span>normal_distribution()</h2>
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template<typename _RealType = double> </div>
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<td class="memname"><a class="el" href="a06311.html">std::normal_distribution</a>< _RealType >::<a class="el" href="a06311.html">normal_distribution</a> </td>
<td>(</td>
<td class="paramtype"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> </td>
<td class="paramname"><em>__mean</em> = <code><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a>(0)</code>, </td>
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<td class="paramname"><em>__stddev</em> = <code><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a>(1)</code> </td>
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<p>Constructs a normal distribution with parameters <img class="formulaInl" alt="$mean$" src="form_32.png"/> and standard deviation. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l01975">1975</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#ae433f04f988a93f6e835d7cf7fbbde31">◆ </a></span>max()</h2>
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template<typename _RealType = double> </div>
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<td class="memname"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType >::max </td>
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<p>Returns the least upper bound value of the distribution. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l02032">2032</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#abcc6e9b8ff25f5d1e076cb5f51f42231">◆ </a></span>mean()</h2>
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template<typename _RealType = double> </div>
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<p>Returns the mean of the distribution. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l01996">1996</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#aa79e79b65edcb6f45dda08b3efdff9e8">◆ </a></span>min()</h2>
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template<typename _RealType = double> </div>
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<p>Returns the greatest lower bound value of the distribution. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l02025">2025</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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template<typename _RealType = double> </div>
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template<typename _UniformRandomNumberGenerator > </div>
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<td class="memname"><a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType >::operator() </td>
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<p>Generating functions. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l02040">2040</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
<p class="reference">Referenced by <a class="el" href="a00452_source.html#l02040">std::normal_distribution< result_type >::operator()()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a159f2f44c19a01c99cb937297d03604c">◆ </a></span>operator()() <span class="overload">[2/2]</span></h2>
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template<typename _RealType > </div>
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<td class="memname"><a class="el" href="a06311.html">normal_distribution</a>< _RealType >::<a class="el" href="a06311.html#ae45488abda3f5b20d944da2da5a70001">result_type</a> <a class="el" href="a06311.html">std::normal_distribution</a>< _RealType >::operator() </td>
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<p>Polar method due to Marsaglia.</p>
<p>Devroye, L. Non-Uniform Random Variates Generation. Springer-Verlag, New York, 1986, Ch. V, Sect. 4.4. </p>
<p class="definition">Definition at line <a class="el" href="a17058_source.html#l01786">1786</a> of file <a class="el" href="a17058_source.html">bits/random.tcc</a>.</p>
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<p>Returns the parameter set of the distribution. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l02010">2010</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<p>Sets the parameter set of the distribution. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<p class="definition">Definition at line <a class="el" href="a00452_source.html#l02018">2018</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a757217130ef7b0eb980500afc8bd865c">◆ </a></span>reset()</h2>
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<p>Resets the distribution state. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l01989">1989</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
<p class="reference">Referenced by <a class="el" href="a00452_source.html#l02199">std::lognormal_distribution< _RealType >::reset()</a>, <a class="el" href="a00452_source.html#l02423">std::gamma_distribution< result_type >::reset()</a>, <a class="el" href="a00452_source.html#l03278">std::student_t_distribution< _RealType >::reset()</a>, <a class="el" href="a00452_source.html#l03734">std::binomial_distribution< _IntType >::reset()</a>, and <a class="el" href="a00452_source.html#l04393">std::poisson_distribution< _IntType >::reset()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#a43aa93573bdffbacfde869b5a11bed31">◆ </a></span>stddev()</h2>
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<p>Returns the standard deviation of the distribution. </p>
<p class="definition">Definition at line <a class="el" href="a00452_source.html#l02003">2003</a> of file <a class="el" href="a00452_source.html">random.h</a>.</p>
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<h2 class="groupheader">Friends And Related Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#abdfecf8325ed9e856625871fee2c56a3">◆ </a></span>operator<<</h2>
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template<typename _RealType = double> </div>
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<p>Inserts a normal_distribution random number distribution <code>__x</code> into the output stream <code>__os</code>. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">__os</td><td>An output stream. </td></tr>
<tr><td class="paramname">__x</td><td>A normal_distribution random number distribution.</td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The output stream with the state of <code>__x</code> inserted or in an error state. </dd></dl>
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<h2 class="memtitle"><span class="permalink"><a href="#afaafdb22ede1508109622f89f50e213d">◆ </a></span>operator==</h2>
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template<typename _RealType = double> </div>
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<p>Return true if two normal distributions have the same parameters and the sequences that would be generated are equal. </p>
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<p>Extracts a normal_distribution random number distribution <code>__x</code> from the input stream <code>__is</code>. </p>
<dl class="params"><dt>Parameters</dt><dd>
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<tr><td class="paramname">__x</td><td>A normal_distribution random number generator engine.</td></tr>
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<dl class="section return"><dt>Returns</dt><dd>The input stream with <code>__x</code> extracted or in an error state. </dd></dl>
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<hr/>The documentation for this class was generated from the following files:<ul>
<li><a class="el" href="a00452_source.html">random.h</a></li>
<li><a class="el" href="a17058_source.html">bits/random.tcc</a></li>
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