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<div class="headertitle"><div class="title">exponential_dist.cpp File Reference</div></div>
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<p><a href="https://en.wikipedia.org/wiki/Exponential_distribution" target="_blank">Exponential Distribution</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;stdexcept&gt;</code><br />
<code>#include &lt;string&gt;</code><br />
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Include dependency graph for exponential_dist.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/ded/namespaceprobability.html">probability</a></td></tr>
<tr class="memdesc:d4/ded/namespaceprobability"><td class="mdescLeft">&#160;</td><td class="mdescRight">Probability algorithms. <br /></td></tr>
<tr class="separator:"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/d35/namespaceexponential__dist.html">exponential_dist</a></td></tr>
<tr class="memdesc:d1/d35/namespaceexponential__dist"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for the <a href="https://en.wikipedia.org/wiki/Exponential_distribution" target="_blank">Exponential Distribution</a> algorithm implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a1c8b6e787f72a209ef96c096eedf7afc" id="r_a1c8b6e787f72a209ef96c096eedf7afc"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a1c8b6e787f72a209ef96c096eedf7afc">probability::geometric_dist::exponential_expected</a> (double lambda)</td></tr>
<tr class="memdesc:a1c8b6e787f72a209ef96c096eedf7afc"><td class="mdescLeft">&#160;</td><td class="mdescRight">the expected value of the exponential distribution <br /></td></tr>
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<tr class="memitem:af435dbeb43a05c8c7785f53bf4ce1df1" id="r_af435dbeb43a05c8c7785f53bf4ce1df1"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af435dbeb43a05c8c7785f53bf4ce1df1">probability::geometric_dist::exponential_var</a> (double lambda)</td></tr>
<tr class="memdesc:af435dbeb43a05c8c7785f53bf4ce1df1"><td class="mdescLeft">&#160;</td><td class="mdescRight">the variance of the exponential distribution <br /></td></tr>
<tr class="separator:af435dbeb43a05c8c7785f53bf4ce1df1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac7b0091e17479d47438a281fefc2549a" id="r_ac7b0091e17479d47438a281fefc2549a"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ac7b0091e17479d47438a281fefc2549a">probability::geometric_dist::exponential_std</a> (double lambda)</td></tr>
<tr class="memdesc:ac7b0091e17479d47438a281fefc2549a"><td class="mdescLeft">&#160;</td><td class="mdescRight">the standard deviation of the exponential distribution <br /></td></tr>
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<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<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>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></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/Exponential_distribution" target="_blank">Exponential Distribution</a> </p>
<p>The exponential distribution is used to model events occuring between a Poisson process like radioactive decay.</p>
<p class="formulaDsp">
\[P(x, \lambda) = \lambda e^{-\lambda x}\]
</p>
<p>Summary of variables used: \(\lambda\) : rate parameter </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a1c8b6e787f72a209ef96c096eedf7afc" name="a1c8b6e787f72a209ef96c096eedf7afc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a1c8b6e787f72a209ef96c096eedf7afc">&#9670;&#160;</a></span>exponential_expected()</h2>
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<td class="memname">double probability::geometric_dist::exponential_expected </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>lambda</em></span></td><td>)</td>
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<p>the expected value of the exponential distribution </p>
<dl class="section return"><dt>Returns</dt><dd><p class="formulaDsp">
\[\mu = \frac{1}{\lambda}\]
</p>
</dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 37</span> {</div>
<div class="line"><span class="lineno"> 38</span> <span class="keywordflow">if</span> (lambda &lt;= 0) {</div>
<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;lambda must be greater than 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 40</span> }</div>
<div class="line"><span class="lineno"> 41</span> <span class="keywordflow">return</span> 1 / lambda;</div>
<div class="line"><span class="lineno"> 42</span>}</div>
<div class="ttc" id="ainvalid_argument_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac7b0091e17479d47438a281fefc2549a">&#9670;&#160;</a></span>exponential_std()</h2>
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<td class="memname">double probability::geometric_dist::exponential_std </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>lambda</em></span></td><td>)</td>
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<p>the standard deviation of the exponential distribution </p>
<dl class="section return"><dt>Returns</dt><dd><p class="formulaDsp">
\[\sigma = \frac{1}{\lambda}\]
</p>
</dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 59</span> {</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordflow">if</span> (lambda &lt;= 0) {</div>
<div class="line"><span class="lineno"> 61</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;lambda must be greater than 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 62</span> }</div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">return</span> 1 / lambda;</div>
<div class="line"><span class="lineno"> 64</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#af435dbeb43a05c8c7785f53bf4ce1df1">&#9670;&#160;</a></span>exponential_var()</h2>
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<td class="memname">double probability::geometric_dist::exponential_var </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>lambda</em></span></td><td>)</td>
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<p>the variance of the exponential distribution </p>
<dl class="section return"><dt>Returns</dt><dd><p class="formulaDsp">
\[\sigma^2 = \frac{1}{\lambda^2}\]
</p>
</dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 48</span> {</div>
<div class="line"><span class="lineno"> 49</span> <span class="keywordflow">if</span> (lambda &lt;= 0) {</div>
<div class="line"><span class="lineno"> 50</span> <span class="keywordflow">throw</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>(<span class="stringliteral">&quot;lambda must be greater than 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 51</span> }</div>
<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">return</span> 1 / <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">pow</a>(lambda, 2);</div>
<div class="line"><span class="lineno"> 53</span>}</div>
<div class="ttc" id="apow_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a></div><div class="ttdeci">T pow(T... args)</div></div>
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<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>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 148</span> {</div>
<div class="line"><span class="lineno"> 149</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Self test implementation</span></div>
<div class="line"><span class="lineno"> 150</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 151</span>}</div>
<div class="ttc" id="aexponential__dist_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> exponential_dist.cpp:72</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">static void test </td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Self-test implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><span class="lineno"> 72</span> {</div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">double</span> lambda_1 = 1;</div>
<div class="line"><span class="lineno"> 74</span> <span class="keywordtype">double</span> expected_1 = 1;</div>
<div class="line"><span class="lineno"> 75</span> <span class="keywordtype">double</span> var_1 = 1;</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordtype">double</span> std_1 = 1;</div>
<div class="line"><span class="lineno"> 77</span> </div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordtype">double</span> lambda_2 = 2;</div>
<div class="line"><span class="lineno"> 79</span> <span class="keywordtype">double</span> expected_2 = 0.5;</div>
<div class="line"><span class="lineno"> 80</span> <span class="keywordtype">double</span> var_2 = 0.25;</div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordtype">double</span> std_2 = 0.5;</div>
<div class="line"><span class="lineno"> 82</span> </div>
<div class="line"><span class="lineno"> 83</span> <span class="keywordtype">double</span> lambda_3 = 3;</div>
<div class="line"><span class="lineno"> 84</span> <span class="keywordtype">double</span> expected_3 = 0.333333;</div>
<div class="line"><span class="lineno"> 85</span> <span class="keywordtype">double</span> var_3 = 0.111111;</div>
<div class="line"><span class="lineno"> 86</span> <span class="keywordtype">double</span> std_3 = 0.333333;</div>
<div class="line"><span class="lineno"> 87</span> </div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordtype">double</span> lambda_4 = 0; <span class="comment">// Test 0</span></div>
<div class="line"><span class="lineno"> 89</span> <span class="keywordtype">double</span> lambda_5 = -2.3; <span class="comment">// Test negative value</span></div>
<div class="line"><span class="lineno"> 90</span> </div>
<div class="line"><span class="lineno"> 91</span> <span class="keyword">const</span> <span class="keywordtype">float</span> threshold = 1e-3f;</div>
<div class="line"><span class="lineno"> 92</span> </div>
<div class="line"><span class="lineno"> 93</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for lambda = 1 \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 94</span> assert(</div>
<div class="line"><span class="lineno"> 95</span> std::abs(expected_1 - probability::geometric_dist::exponential_expected(</div>
<div class="line"><span class="lineno"> 96</span> lambda_1)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 97</span> assert(std::abs(var_1 - probability::geometric_dist::exponential_var(</div>
<div class="line"><span class="lineno"> 98</span> lambda_1)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 99</span> assert(std::abs(std_1 - probability::geometric_dist::exponential_std(</div>
<div class="line"><span class="lineno"> 100</span> lambda_1)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 101</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ALL TEST PASSED\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 102</span> </div>
<div class="line"><span class="lineno"> 103</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for lambda = 2 \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 104</span> assert(</div>
<div class="line"><span class="lineno"> 105</span> std::abs(expected_2 - probability::geometric_dist::exponential_expected(</div>
<div class="line"><span class="lineno"> 106</span> lambda_2)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 107</span> assert(std::abs(var_2 - probability::geometric_dist::exponential_var(</div>
<div class="line"><span class="lineno"> 108</span> lambda_2)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 109</span> assert(std::abs(std_2 - probability::geometric_dist::exponential_std(</div>
<div class="line"><span class="lineno"> 110</span> lambda_2)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 111</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ALL TEST PASSED\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 112</span> </div>
<div class="line"><span class="lineno"> 113</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for lambda = 3 \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 114</span> assert(</div>
<div class="line"><span class="lineno"> 115</span> std::abs(expected_3 - probability::geometric_dist::exponential_expected(</div>
<div class="line"><span class="lineno"> 116</span> lambda_3)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 117</span> assert(std::abs(var_3 - probability::geometric_dist::exponential_var(</div>
<div class="line"><span class="lineno"> 118</span> lambda_3)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 119</span> assert(std::abs(std_3 - probability::geometric_dist::exponential_std(</div>
<div class="line"><span class="lineno"> 120</span> lambda_3)) &lt; threshold);</div>
<div class="line"><span class="lineno"> 121</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ALL TEST PASSED\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 122</span> </div>
<div class="line"><span class="lineno"> 123</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for lambda = 0 \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 124</span> <span class="keywordflow">try</span> {</div>
<div class="line"><span class="lineno"> 125</span> <a class="code hl_function" href="#a1c8b6e787f72a209ef96c096eedf7afc">probability::geometric_dist::exponential_expected</a>(lambda_4);</div>
<div class="line"><span class="lineno"> 126</span> <a class="code hl_function" href="#af435dbeb43a05c8c7785f53bf4ce1df1">probability::geometric_dist::exponential_var</a>(lambda_4);</div>
<div class="line"><span class="lineno"> 127</span> <a class="code hl_function" href="#ac7b0091e17479d47438a281fefc2549a">probability::geometric_dist::exponential_std</a>(lambda_4);</div>
<div class="line"><span class="lineno"> 128</span> } <span class="keywordflow">catch</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>&amp; err) {</div>
<div class="line"><span class="lineno"> 129</span> assert(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(err.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/exception/what.html">what</a>()) == <span class="stringliteral">&quot;lambda must be greater than 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 130</span> }</div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ALL TEST PASSED\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 132</span> </div>
<div class="line"><span class="lineno"> 133</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;Test for lambda = -2.3 \n&quot;</span>;</div>
<div class="line"><span class="lineno"> 134</span> <span class="keywordflow">try</span> {</div>
<div class="line"><span class="lineno"> 135</span> <a class="code hl_function" href="#a1c8b6e787f72a209ef96c096eedf7afc">probability::geometric_dist::exponential_expected</a>(lambda_5);</div>
<div class="line"><span class="lineno"> 136</span> <a class="code hl_function" href="#af435dbeb43a05c8c7785f53bf4ce1df1">probability::geometric_dist::exponential_var</a>(lambda_5);</div>
<div class="line"><span class="lineno"> 137</span> <a class="code hl_function" href="#ac7b0091e17479d47438a281fefc2549a">probability::geometric_dist::exponential_std</a>(lambda_5);</div>
<div class="line"><span class="lineno"> 138</span> } <span class="keywordflow">catch</span> (<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/invalid_argument.html">std::invalid_argument</a>&amp; err) {</div>
<div class="line"><span class="lineno"> 139</span> assert(<a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a>(err.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/error/exception/what.html">what</a>()) == <span class="stringliteral">&quot;lambda must be greater than 0&quot;</span>);</div>
<div class="line"><span class="lineno"> 140</span> }</div>
<div class="line"><span class="lineno"> 141</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; <span class="stringliteral">&quot;ALL TEST PASSED\n\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 142</span>}</div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="abasic_string_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/string/basic_string.html">std::string</a></div></div>
<div class="ttc" id="aexponential__dist_8cpp_html_a1c8b6e787f72a209ef96c096eedf7afc"><div class="ttname"><a href="#a1c8b6e787f72a209ef96c096eedf7afc">probability::geometric_dist::exponential_expected</a></div><div class="ttdeci">double exponential_expected(double lambda)</div><div class="ttdoc">the expected value of the exponential distribution</div><div class="ttdef"><b>Definition</b> exponential_dist.cpp:37</div></div>
<div class="ttc" id="aexponential__dist_8cpp_html_ac7b0091e17479d47438a281fefc2549a"><div class="ttname"><a href="#ac7b0091e17479d47438a281fefc2549a">probability::geometric_dist::exponential_std</a></div><div class="ttdeci">double exponential_std(double lambda)</div><div class="ttdoc">the standard deviation of the exponential distribution</div><div class="ttdef"><b>Definition</b> exponential_dist.cpp:59</div></div>
<div class="ttc" id="aexponential__dist_8cpp_html_af435dbeb43a05c8c7785f53bf4ce1df1"><div class="ttname"><a href="#af435dbeb43a05c8c7785f53bf4ce1df1">probability::geometric_dist::exponential_var</a></div><div class="ttdeci">double exponential_var(double lambda)</div><div class="ttdoc">the variance of the exponential distribution</div><div class="ttdef"><b>Definition</b> exponential_dist.cpp:48</div></div>
<div class="ttc" id="awhat_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/error/exception/what.html">std::invalid_argument::what</a></div><div class="ttdeci">T what(T... args)</div></div>
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