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<p><a href="https://en.wikipedia.org/wiki/Poisson_distribution">Poisson statistics</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
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Include dependency graph for poisson_dist.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:ac217ab9a06291f360d816700a6958ca8"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a> (double events, double timeframe)</td></tr>
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<tr class="memitem:ad0aa718023ce802dd5899f0e03a7ac71"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a> (double rate, double time)</td></tr>
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<tr class="memitem:a63ffd347e75d5ed7a518cbcfbfeec71a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a> (double x)</td></tr>
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<tr class="memitem:a69a136b32707bdc7950fb9057b5fa1e1"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a> (double expected, double x)</td></tr>
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<tr class="memitem:ad9c9e74079278ca10e3b97a8d5391c9a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a> (double expected, double lower, double upper)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d9/d24/poisson__dist_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Poisson_distribution">Poisson statistics</a> </p>
<p>The Poisson distribution counts how many events occur over a set time interval. </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a63ffd347e75d5ed7a518cbcfbfeec71a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a63ffd347e75d5ed7a518cbcfbfeec71a">&#9670;&nbsp;</a></span>fact()</h2>
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<td class="memname">double fact </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
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<p>Compute factorial of a given number </p>
<div class="fragment"><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160; {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; <span class="keywordtype">double</span> x_fact = x;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = x - 1; i &gt; 0; i--) {</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; x_fact *= i;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160; }</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">if</span> (x_fact &lt;= 0) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; x_fact = 1;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; }</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">return</span> x_fact;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
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<p>main function </p>
<div class="fragment"><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordtype">double</span> rate, expected;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; rate = <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a>(3, 1);</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson rate : &quot;</span> &lt;&lt; rate &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; expected = <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a>(rate, 2);</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson expected : &quot;</span> &lt;&lt; expected &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson 0 successes : &quot;</span> &lt;&lt; <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, 0)</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Poisson 0-8 successes : &quot;</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; &lt;&lt; <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a>(expected, 0, 8) &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ad0aa718023ce802dd5899f0e03a7ac71">&#9670;&nbsp;</a></span>poisson_expected()</h2>
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<td class="memname">double poisson_expected </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>rate</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>time</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>calculate the expected value over a time e.g rate of 2.5 over 10 mins = 2.5 x 10 = 25 </p>
<div class="fragment"><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;{ <span class="keywordflow">return</span> rate * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">time</a>; }</div>
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<a id="ad9c9e74079278ca10e3b97a8d5391c9a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad9c9e74079278ca10e3b97a8d5391c9a">&#9670;&nbsp;</a></span>poisson_range_successes()</h2>
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<td class="memname">double poisson_range_successes </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>expected</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>lower</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>upper</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
<td></td><td></td>
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<p>probability of a success in range for Poisson dist (inclusive, inclusive) </p><p class="formulaDsp">
\[P = \sum_i p(\mu,i)\]
</p>
<div class="fragment"><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordtype">double</span> probability = 0;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower; i &lt;= upper; i++) {</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; probability += <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, i);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; }</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; <span class="keywordflow">return</span> probability;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac217ab9a06291f360d816700a6958ca8">&#9670;&nbsp;</a></span>poisson_rate()</h2>
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<td class="memname">double poisson_rate </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>events</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>timeframe</em>&#160;</td>
</tr>
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<td></td>
<td>)</td>
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<p>poisson rate:<br />
calculate the events per unit time<br />
e.g 5 dollars every 2 mins = 5 / 2 = 2.5 </p>
<div class="fragment"><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160; {</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160; <span class="keywordflow">return</span> events / timeframe;</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;}</div>
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<a id="a69a136b32707bdc7950fb9057b5fa1e1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a69a136b32707bdc7950fb9057b5fa1e1">&#9670;&nbsp;</a></span>poisson_x_successes()</h2>
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<td class="memname">double poisson_x_successes </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>expected</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x</em>&#160;</td>
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<td>)</td>
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</div><div class="memdoc">
<p>Find the probability of x successes in a Poisson dist. </p><p class="formulaDsp">
\[p(\mu,x) = \frac{\mu^x e^{-\mu}}{x!}\]
</p>
<div class="fragment"><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; <span class="keywordflow">return</span> (<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(expected, x) * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/exp.html">std::exp</a>(-expected)) / <a class="code" href="../../d9/d24/poisson__dist_8cpp.html#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a>(x);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;}</div>
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