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<div class="header">
<div class="summary">
<a href="#func-members">Functions</a> </div>
<div class="headertitle">
<div class="title">statistics.h File Reference</div> </div>
</div><!--header-->
<div class="contents">
<p>Statistics related functions.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include <cmath></code><br />
<code>#include <cstdlib></code><br />
<code>#include <numeric></code><br />
<code>#include <random></code><br />
<code>#include <vector></code><br />
</div>
<p><a href="statistics_8h_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a5f5fe8a2a3555ff017c506d28155484e"><td class="memTemplParams" colspan="2">template<typename T = long double> </td></tr>
<tr class="memitem:a5f5fe8a2a3555ff017c506d28155484e"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="statistics_8h.html#a5f5fe8a2a3555ff017c506d28155484e">Statistics::runif</a> (const T &a=0, const T &b=1)</td></tr>
<tr class="memdesc:a5f5fe8a2a3555ff017c506d28155484e"><td class="mdescLeft"> </td><td class="mdescRight">Uniform number generator. <a href="statistics_8h.html#a5f5fe8a2a3555ff017c506d28155484e">More...</a><br /></td></tr>
<tr class="separator:a5f5fe8a2a3555ff017c506d28155484e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a73c2bf1eef16a529e48b473e99d5dd14"><td class="memTemplParams" colspan="2">template<typename T = long double> </td></tr>
<tr class="memitem:a73c2bf1eef16a529e48b473e99d5dd14"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="statistics_8h.html#a73c2bf1eef16a529e48b473e99d5dd14">Statistics::rnorm</a> (const T &mean=0, const T &sd=1)</td></tr>
<tr class="memdesc:a73c2bf1eef16a529e48b473e99d5dd14"><td class="mdescLeft"> </td><td class="mdescRight">Normal number generator with Box–Muller transform. <a href="statistics_8h.html#a73c2bf1eef16a529e48b473e99d5dd14">More...</a><br /></td></tr>
<tr class="separator:a73c2bf1eef16a529e48b473e99d5dd14"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a027a33acc5f9aaedee6c3c81c8bd0bae"><td class="memTemplParams" colspan="2">template<typename T = long double> </td></tr>
<tr class="memitem:a027a33acc5f9aaedee6c3c81c8bd0bae"><td class="memTemplItemLeft" align="right" valign="top">T </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="statistics_8h.html#a027a33acc5f9aaedee6c3c81c8bd0bae">Statistics::pchisq</a> (const T &stat, const unsigned int &k)</td></tr>
<tr class="memdesc:a027a33acc5f9aaedee6c3c81c8bd0bae"><td class="mdescLeft"> </td><td class="mdescRight">Chi-Squared distribution. <a href="statistics_8h.html#a027a33acc5f9aaedee6c3c81c8bd0bae">More...</a><br /></td></tr>
<tr class="separator:a027a33acc5f9aaedee6c3c81c8bd0bae"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1518ff4401fd83f58e6f0b67f185b7dc"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="statistics_8h.html#a1518ff4401fd83f58e6f0b67f185b7dc">Statistics::jb_test</a> (const std::vector< long double > &x)</td></tr>
<tr class="memdesc:a1518ff4401fd83f58e6f0b67f185b7dc"><td class="mdescLeft"> </td><td class="mdescRight">Jarque–Bera test. <a href="statistics_8h.html#a1518ff4401fd83f58e6f0b67f185b7dc">More...</a><br /></td></tr>
<tr class="separator:a1518ff4401fd83f58e6f0b67f185b7dc"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Statistics related functions. </p>
<dl class="section author"><dt>Author</dt><dd>Murat Koptur <a href="#" onclick="location.href='mai'+'lto:'+'mko'+'pt'+'ur3'+'@g'+'mai'+'l.'+'com'; return false;">mkopt<span style="display: none;">.nosp@m.</span>ur3@<span style="display: none;">.nosp@m.</span>gmail<span style="display: none;">.nosp@m.</span>.com</a></dd></dl>
<p>Last updated: 22/Jan/2019. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="file_a1518ff4401fd83f58e6f0b67f185b7dc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a1518ff4401fd83f58e6f0b67f185b7dc">◆ </a></span>jb_test()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">bool Statistics::jb_test </td>
<td>(</td>
<td class="paramtype">const std::vector< long double > & </td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Jarque–Bera test. </p>
<p>Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>Vector of numbers.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A boolean which indicates that x is normally distributed or not. </dd></dl>
</div>
</div>
<a id="file_a027a33acc5f9aaedee6c3c81c8bd0bae"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a027a33acc5f9aaedee6c3c81c8bd0bae">◆ </a></span>pchisq()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T = long double> </div>
<table class="memname">
<tr>
<td class="memname">T Statistics::pchisq </td>
<td>(</td>
<td class="paramtype">const T & </td>
<td class="paramname"><em>stat</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const unsigned int & </td>
<td class="paramname"><em>k</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Chi-Squared distribution. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">stat</td><td>Test statistic. </td></tr>
<tr><td class="paramname">k</td><td>Degrees of freedom.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A probability. </dd></dl>
</div>
</div>
<a id="file_a73c2bf1eef16a529e48b473e99d5dd14"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a73c2bf1eef16a529e48b473e99d5dd14">◆ </a></span>rnorm()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T = long double> </div>
<table class="memname">
<tr>
<td class="memname">T Statistics::rnorm </td>
<td>(</td>
<td class="paramtype">const T & </td>
<td class="paramname"><em>mean</em> = <code>0</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const T & </td>
<td class="paramname"><em>sd</em> = <code>1</code> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Normal number generator with Box–Muller transform. </p>
<p>Box–Muller transform is a pseudo-random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">mean</td><td>Mean of distribution. </td></tr>
<tr><td class="paramname">sd</td><td>Standart deviation of distribution.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A random number. </dd></dl>
</div>
</div>
<a id="file_a5f5fe8a2a3555ff017c506d28155484e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#file_a5f5fe8a2a3555ff017c506d28155484e">◆ </a></span>runif()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template<typename T = long double> </div>
<table class="memname">
<tr>
<td class="memname">T Statistics::runif </td>
<td>(</td>
<td class="paramtype">const T & </td>
<td class="paramname"><em>a</em> = <code>0</code>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const T & </td>
<td class="paramname"><em>b</em> = <code>1</code> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Uniform number generator. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">a</td><td>Lower bound. </td></tr>
<tr><td class="paramname">b</td><td>Upper bound.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A random number between [a, b]. </dd></dl>
</div>
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