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<title>Algorithms_in_C++: probability::geometric_dist::geometric_distribution Class Reference</title>
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<div id="projectname">Algorithms_in_C++<span id="projectnumber"> 1.0.0</span>
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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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@@ -172,7 +172,7 @@ float </td><td class="memItemRight" valign="bottom"><b>p</b></td></tr>
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<div class="fragment"><div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span>: <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>(<a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>) {}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 64</span>: <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>(<a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>) {}</div>
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<div class="ttc" id="aclassprobability_1_1geometric__dist_1_1geometric__distribution_html_ad5ed23a251dbe55ad1ed06bf1a465ad3"><div class="ttname"><a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">probability::geometric_dist::geometric_distribution::p</a></div><div class="ttdeci">float p</div><div class="ttdoc">The succes probability p.</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:57</div></div>
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@@ -210,9 +210,9 @@ float </td><td class="memItemRight" valign="bottom"><b>p</b></td></tr>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>The probability to have success within k trials </dd></dl>
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<div class="fragment"><div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> {</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="keywordflow">return</span> 1.0f - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>((1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>), <span class="keyword">static_cast<</span><span class="keywordtype">float</span><span class="keyword">></span>(k));</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 104</span> {</div>
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<div class="line"><span class="lineno"> 105</span> <span class="keywordflow">return</span> 1.0f - <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>((1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>), <span class="keyword">static_cast<</span><span class="keywordtype">float</span><span class="keyword">></span>(k));</div>
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<div class="line"><span class="lineno"> 106</span> }</div>
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<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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<p>Generates a (discrete) sample according to the geometrical distribution. </p>
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<dl class="section return"><dt>Returns</dt><dd>A geometrically distributed number in [1,\infty) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> {</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordtype">float</span> uniform_sample = <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba">generate_uniform</a>();</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="keywordflow">return</span> <span class="keyword">static_cast<</span>uint32_t<span class="keyword">></span>(</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aaf762e88c66918d7afda4234f28a7ddf">inverse_cumulative_distribution</a>(uniform_sample)) +</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> 1;</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 125</span> {</div>
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<div class="line"><span class="lineno"> 126</span> <span class="keywordtype">float</span> uniform_sample = <a class="code hl_function" href="../../de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba">generate_uniform</a>();</div>
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<div class="line"><span class="lineno"> 127</span> <span class="keywordflow">return</span> <span class="keyword">static_cast<</span>uint32_t<span class="keyword">></span>(</div>
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<div class="line"><span class="lineno"> 128</span> <a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aaf762e88c66918d7afda4234f28a7ddf">inverse_cumulative_distribution</a>(uniform_sample)) +</div>
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<div class="line"><span class="lineno"> 129</span> 1;</div>
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<div class="line"><span class="lineno"> 130</span> }</div>
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<div class="ttc" id="aclassprobability_1_1geometric__dist_1_1geometric__distribution_html_aaf762e88c66918d7afda4234f28a7ddf"><div class="ttname"><a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aaf762e88c66918d7afda4234f28a7ddf">probability::geometric_dist::geometric_distribution::inverse_cumulative_distribution</a></div><div class="ttdeci">float inverse_cumulative_distribution(const float &cdf) const</div><div class="ttdoc">The inverse cumulative distribution function.</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:116</div></div>
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<div class="ttc" id="ageometric__dist_8cpp_html_a82964ca6180507deb5fafc71050012ba"><div class="ttname"><a href="../../de/d72/geometric__dist_8cpp.html#a82964ca6180507deb5fafc71050012ba">probability::geometric_dist::generate_uniform</a></div><div class="ttdeci">float generate_uniform()</div><div class="ttdoc">Returns a random number between [0,1].</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:48</div></div>
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<p>The expected value of a geometrically distributed random variable X. </p>
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<dl class="section return"><dt>Returns</dt><dd>E[X] = 1/p </dd></dl>
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<div class="fragment"><div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span>{ <span class="keywordflow">return</span> 1.0f / <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>; }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 71</span>{ <span class="keywordflow">return</span> 1.0f / <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>; }</div>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>The number of (exact) trials. </dd></dl>
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<div class="fragment"><div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> {</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(1.0f - cdf) / <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>);</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 116</span> {</div>
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<div class="line"><span class="lineno"> 117</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(1.0f - cdf) / <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a>(1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>);</div>
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<div class="line"><span class="lineno"> 118</span> }</div>
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<div class="ttc" id="alog_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/log.html">std::log</a></div><div class="ttdeci">T log(T... args)</div></div>
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</dd>
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<dl class="section return"><dt>Returns</dt><dd>A number between [0,1] according to p * (1-p)^{k-1} </dd></dl>
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<div class="fragment"><div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> {</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>((1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>), <span class="keyword">static_cast<</span><span class="keywordtype">float</span><span class="keyword">></span>(k - 1)) * <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>;</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 93</span> {</div>
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<div class="line"><span class="lineno"> 94</span> <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>((1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>), <span class="keyword">static_cast<</span><span class="keywordtype">float</span><span class="keyword">></span>(k - 1)) * <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>;</div>
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<div class="line"><span class="lineno"> 95</span> }</div>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>The probability of having success within a range of tries [min_tries, max_tries] </dd></dl>
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<div class="fragment"><div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> {</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> <span class="keywordtype">float</span> cdf_lower = <a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">cumulative_distribution</a>(min_tries - 1);</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordtype">float</span> cdf_upper = max_tries == <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits<uint32_t>::max</a>()</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> ? 1.0f</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> : <a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">cumulative_distribution</a>(max_tries);</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">return</span> cdf_upper - cdf_lower;</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 147</span> {</div>
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<div class="line"><span class="lineno"> 148</span> <span class="keywordtype">float</span> cdf_lower = <a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">cumulative_distribution</a>(min_tries - 1);</div>
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<div class="line"><span class="lineno"> 149</span> <span class="keywordtype">float</span> cdf_upper = max_tries == <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits<uint32_t>::max</a>()</div>
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<div class="line"><span class="lineno"> 150</span> ? 1.0f</div>
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<div class="line"><span class="lineno"> 151</span> : <a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">cumulative_distribution</a>(max_tries);</div>
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<div class="line"><span class="lineno"> 152</span> <span class="keywordflow">return</span> cdf_upper - cdf_lower;</div>
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<div class="line"><span class="lineno"> 153</span> }</div>
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<div class="ttc" id="aclassprobability_1_1geometric__dist_1_1geometric__distribution_html_a08328dc7d62188427111f176b56a105a"><div class="ttname"><a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#a08328dc7d62188427111f176b56a105a">probability::geometric_dist::geometric_distribution::cumulative_distribution</a></div><div class="ttdeci">float cumulative_distribution(const uint32_t &k) const</div><div class="ttdoc">The cumulative distribution function.</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:104</div></div>
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<div class="ttc" id="amax_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/types/numeric_limits/max.html">std::numeric_limits::max</a></div><div class="ttdeci">T max(T... args)</div></div>
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<p>The standard deviation of a geometrically distributed random variable X. </p>
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<dl class="section return"><dt>Returns</dt><dd>\sigma = \sqrt{V[X]} </dd></dl>
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<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960">variance</a>()); }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 84</span>{ <span class="keywordflow">return</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a>(<a class="code hl_function" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960">variance</a>()); }</div>
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<div class="ttc" id="aclassprobability_1_1geometric__dist_1_1geometric__distribution_html_aea8b0d649f0dc9a6f8baf3341a0b4960"><div class="ttname"><a href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#aea8b0d649f0dc9a6f8baf3341a0b4960">probability::geometric_dist::geometric_distribution::variance</a></div><div class="ttdeci">float variance() const</div><div class="ttdoc">The variance of a geometrically distributed random variable X.</div><div class="ttdef"><b>Definition:</b> geometric_dist.cpp:77</div></div>
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<div class="ttc" id="asqrt_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/math/sqrt.html">std::sqrt</a></div><div class="ttdeci">T sqrt(T... args)</div></div>
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<p>The variance of a geometrically distributed random variable X. </p>
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<dl class="section return"><dt>Returns</dt><dd>V[X] = (1 - p) / p^2 </dd></dl>
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<div class="fragment"><div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span>{ <span class="keywordflow">return</span> (1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>) / (<a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a> * <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>); }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 77</span>{ <span class="keywordflow">return</span> (1.0f - <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>) / (<a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a> * <a class="code hl_variable" href="../../da/d19/classprobability_1_1geometric__dist_1_1geometric__distribution.html#ad5ed23a251dbe55ad1ed06bf1a465ad3">p</a>); }</div>
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