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<p><a href="https://en.wikipedia.org/wiki/Poisson_distribution" target="_blank">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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<p><a href="../../d9/d24/poisson__dist_8cpp_source.html">Go to the source code of this file.</a></p>
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Functions</h2></td></tr>
<tr class="memitem:ac217ab9a06291f360d816700a6958ca8" id="r_ac217ab9a06291f360d816700a6958ca8"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a> (double events, double timeframe)</td></tr>
<tr class="memitem:ad0aa718023ce802dd5899f0e03a7ac71" id="r_ad0aa718023ce802dd5899f0e03a7ac71"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a> (double rate, double time)</td></tr>
<tr class="memitem:a63ffd347e75d5ed7a518cbcfbfeec71a" id="r_a63ffd347e75d5ed7a518cbcfbfeec71a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a> (double x)</td></tr>
<tr class="memitem:a69a136b32707bdc7950fb9057b5fa1e1" id="r_a69a136b32707bdc7950fb9057b5fa1e1"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a> (double expected, double x)</td></tr>
<tr class="memitem:ad9c9e74079278ca10e3b97a8d5391c9a" id="r_ad9c9e74079278ca10e3b97a8d5391c9a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a> (double expected, double <a class="el" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>, double upper)</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Poisson_distribution" target="_blank">Poisson statistics</a> </p>
<p>The Poisson distribution counts how many events occur over a set time interval. </p>
<p class="definition">Definition in file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="a63ffd347e75d5ed7a518cbcfbfeec71a" name="a63ffd347e75d5ed7a518cbcfbfeec71a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a63ffd347e75d5ed7a518cbcfbfeec71a">&#9670;&#160;</a></span>fact()</h2>
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<td class="memname">double fact </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x</em></span></td><td>)</td>
<td></td>
</tr>
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<p>Compute factorial of a given number </p>
<p class="definition">Definition at line <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html#l00030">30</a> of file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 30</span> {</div>
<div class="line"><span class="lineno"> 31</span> <span class="keywordtype">double</span> x_fact = x;</div>
<div class="line"><span class="lineno"> 32</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = x - 1; i &gt; 0; i--) {</div>
<div class="line"><span class="lineno"> 33</span> x_fact *= i;</div>
<div class="line"><span class="lineno"> 34</span> }</div>
<div class="line"><span class="lineno"> 35</span> </div>
<div class="line"><span class="lineno"> 36</span> <span class="keywordflow">if</span> (x_fact &lt;= 0) {</div>
<div class="line"><span class="lineno"> 37</span> x_fact = 1;</div>
<div class="line"><span class="lineno"> 38</span> }</div>
<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">return</span> x_fact;</div>
<div class="line"><span class="lineno"> 40</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
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<p>main function </p>
<p class="definition">Definition at line <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html#l00065">65</a> of file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
<div class="line"><span class="lineno"> 66</span> <span class="keywordtype">double</span> rate, expected;</div>
<div class="line"><span class="lineno"> 67</span> rate = <a class="code hl_function" href="#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a>(3, 1);</div>
<div class="line"><span class="lineno"> 68</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Poisson rate : &quot;</span> &lt;&lt; rate &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 69</span> </div>
<div class="line"><span class="lineno"> 70</span> expected = <a class="code hl_function" href="#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a>(rate, 2);</div>
<div class="line"><span class="lineno"> 71</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Poisson expected : &quot;</span> &lt;&lt; expected &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Poisson 0 successes : &quot;</span> &lt;&lt; <a class="code hl_function" href="#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, 0)</div>
<div class="line"><span class="lineno"> 74</span> &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 75</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Poisson 0-8 successes : &quot;</span></div>
<div class="line"><span class="lineno"> 76</span> &lt;&lt; <a class="code hl_function" href="#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a>(expected, 0, 8) &lt;&lt; std::endl;</div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 79</span>}</div>
<div class="ttc" id="apoisson__dist_8cpp_html_a69a136b32707bdc7950fb9057b5fa1e1"><div class="ttname"><a href="#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a></div><div class="ttdeci">double poisson_x_successes(double expected, double x)</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d24/poisson__dist_8cpp_source.html#l00046">poisson_dist.cpp:46</a></div></div>
<div class="ttc" id="apoisson__dist_8cpp_html_ac217ab9a06291f360d816700a6958ca8"><div class="ttname"><a href="#ac217ab9a06291f360d816700a6958ca8">poisson_rate</a></div><div class="ttdeci">double poisson_rate(double events, double timeframe)</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d24/poisson__dist_8cpp_source.html#l00017">poisson_dist.cpp:17</a></div></div>
<div class="ttc" id="apoisson__dist_8cpp_html_ad0aa718023ce802dd5899f0e03a7ac71"><div class="ttname"><a href="#ad0aa718023ce802dd5899f0e03a7ac71">poisson_expected</a></div><div class="ttdeci">double poisson_expected(double rate, double time)</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d24/poisson__dist_8cpp_source.html#l00025">poisson_dist.cpp:25</a></div></div>
<div class="ttc" id="apoisson__dist_8cpp_html_ad9c9e74079278ca10e3b97a8d5391c9a"><div class="ttname"><a href="#ad9c9e74079278ca10e3b97a8d5391c9a">poisson_range_successes</a></div><div class="ttdeci">double poisson_range_successes(double expected, double lower, double upper)</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d24/poisson__dist_8cpp_source.html#l00054">poisson_dist.cpp:54</a></div></div>
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<a id="ad0aa718023ce802dd5899f0e03a7ac71" name="ad0aa718023ce802dd5899f0e03a7ac71"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad0aa718023ce802dd5899f0e03a7ac71">&#9670;&#160;</a></span>poisson_expected()</h2>
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<td class="memname">double poisson_expected </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>rate</em></span>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>time</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<p>calculate the expected value over a time e.g rate of 2.5 over 10 mins = 2.5 x 10 = 25 </p>
<p class="definition">Definition at line <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html#l00025">25</a> of file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 25</span>{ <span class="keywordflow">return</span> rate * time; }</div>
</div><!-- fragment -->
</div>
</div>
<a id="ad9c9e74079278ca10e3b97a8d5391c9a" name="ad9c9e74079278ca10e3b97a8d5391c9a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ad9c9e74079278ca10e3b97a8d5391c9a">&#9670;&#160;</a></span>poisson_range_successes()</h2>
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<td class="memname">double poisson_range_successes </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>expected</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>lower</em></span>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>upper</em></span>&#160;)</td>
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</table>
</div><div class="memdoc">
<p>probability of a success in range for Poisson dist (inclusive, inclusive) </p><p class="formulaDsp">
\[P = \sum_i p(\mu,i)\]
</p>
<p class="definition">Definition at line <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html#l00054">54</a> of file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 54</span> {</div>
<div class="line"><span class="lineno"> 55</span> <span class="keywordtype">double</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> = 0;</div>
<div class="line"><span class="lineno"> 56</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = <a class="code hl_function" href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a>; i &lt;= upper; i++) {</div>
<div class="line"><span class="lineno"> 57</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="#a69a136b32707bdc7950fb9057b5fa1e1">poisson_x_successes</a>(expected, i);</div>
<div class="line"><span class="lineno"> 58</span> }</div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a>;</div>
<div class="line"><span class="lineno"> 60</span>}</div>
<div class="ttc" id="anamespaceprobability_html"><div class="ttname"><a href="../../d4/ded/namespaceprobability.html">probability</a></div><div class="ttdoc">Probability algorithms.</div></div>
<div class="ttc" id="atext__search_8cpp_html_a3f8975d227cd0e58f298b380c5dac0d9"><div class="ttname"><a href="../../dc/db5/text__search_8cpp.html#a3f8975d227cd0e58f298b380c5dac0d9">lower</a></div><div class="ttdeci">std::string lower(std::string word)</div><div class="ttdoc">function to convert a C++ string to lower case</div><div class="ttdef"><b>Definition</b> <a href="../../dc/db5/text__search_8cpp_source.html#l00019">text_search.cpp:19</a></div></div>
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<a id="ac217ab9a06291f360d816700a6958ca8" name="ac217ab9a06291f360d816700a6958ca8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ac217ab9a06291f360d816700a6958ca8">&#9670;&#160;</a></span>poisson_rate()</h2>
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<td class="memname">double poisson_rate </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>events</em></span>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>timeframe</em></span>&#160;)</td>
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</div><div class="memdoc">
<p>poisson rate:<br />
calculate the events per unit time<br />
e.g 5 dollars every 2 mins = 5 / 2 = 2.5 </p>
<p class="definition">Definition at line <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html#l00017">17</a> of file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 17</span> {</div>
<div class="line"><span class="lineno"> 18</span> <span class="keywordflow">return</span> events / timeframe;</div>
<div class="line"><span class="lineno"> 19</span>}</div>
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<a id="a69a136b32707bdc7950fb9057b5fa1e1" name="a69a136b32707bdc7950fb9057b5fa1e1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a69a136b32707bdc7950fb9057b5fa1e1">&#9670;&#160;</a></span>poisson_x_successes()</h2>
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<td class="memname">double poisson_x_successes </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>expected</em></span>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x</em></span>&#160;)</td>
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<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>
<p class="definition">Definition at line <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html#l00046">46</a> of file <a class="el" href="../../d9/d24/poisson__dist_8cpp_source.html">poisson_dist.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 46</span> {</div>
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">return</span> (std::pow(expected, x) * std::exp(-expected)) / <a class="code hl_function" href="#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a>(x);</div>
<div class="line"><span class="lineno"> 48</span>}</div>
<div class="ttc" id="apoisson__dist_8cpp_html_a63ffd347e75d5ed7a518cbcfbfeec71a"><div class="ttname"><a href="#a63ffd347e75d5ed7a518cbcfbfeec71a">fact</a></div><div class="ttdeci">double fact(double x)</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d24/poisson__dist_8cpp_source.html#l00030">poisson_dist.cpp:30</a></div></div>
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