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<title>Algorithms_in_C++: probability/binomial_dist.cpp File 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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@@ -166,7 +166,7 @@ Functions</h2></td></tr>
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<dl class="section return"><dt>Returns</dt><dd>\(\mu=np\) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span>{ <span class="keywordflow">return</span> n * p; }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 22</span>{ <span class="keywordflow">return</span> n * p; }</div>
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@@ -208,13 +208,13 @@ Functions</h2></td></tr>
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</div><div class="memdoc">
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<p >calculates the probability of a result within a range (inclusive, inclusive) </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle \left.P(n,p)\right|_{x_0}^{x_1} = \sum_{i=x_0}^{x_1} P(i) =\sum_{i=x_0}^{x_1} {n\choose i} p^i (1-p)^{n-i}\) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> {</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">double</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> = 0;</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower_bound; i <= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a>; i++) {</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> }</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a>;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 75</span> {</div>
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<div class="line"><span class="lineno"> 76</span> <span class="keywordtype">double</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> = 0;</div>
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<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = lower_bound; i <= <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/upper_bound.html">upper_bound</a>; i++) {</div>
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<div class="line"><span class="lineno"> 78</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a> += <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, i) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - i);</div>
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<div class="line"><span class="lineno"> 79</span> }</div>
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<div class="line"><span class="lineno"> 80</span> <span class="keywordflow">return</span> <a class="code hl_namespace" href="../../d4/ded/namespaceprobability.html">probability</a>;</div>
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<div class="line"><span class="lineno"> 81</span>}</div>
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<div class="ttc" id="abinomial__dist_8cpp_html_a78d36635232e54b5d71fcbf1eac9a49a"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a></div><div class="ttdeci">double nCr(double n, double r)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:47</div></div>
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<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>
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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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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>\(\sigma = \sqrt{\sigma^2} = \sqrt{n\cdot p\cdot (1-p)}\) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> {</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</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="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 36</span> {</div>
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<div class="line"><span class="lineno"> 37</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="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(n, p));</div>
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<div class="line"><span class="lineno"> 38</span>}</div>
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<div class="ttc" id="abinomial__dist_8cpp_html_acd4dd4558031e4c5d045c801f73d8861"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a></div><div class="ttdeci">double binomial_variance(double n, double p)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:29</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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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>\(\sigma^2 = n\cdot p\cdot (1-p)\) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span>{ <span class="keywordflow">return</span> n * p * (1 - p); }</div>
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<div class="fragment"><div class="line"><span class="lineno"> 29</span>{ <span class="keywordflow">return</span> n * p * (1 - p); }</div>
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<p >calculates the probability of exactly x successes </p><dl class="section return"><dt>Returns</dt><dd>\(\displaystyle P(n,p,x) = {n\choose x} p^x (1-p)^{n-x}\) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> {</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 65</span> {</div>
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<div class="line"><span class="lineno"> 66</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a78d36635232e54b5d71fcbf1eac9a49a">nCr</a>(n, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(p, x) * <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/pow.html">std::pow</a>(1 - p, n - x);</div>
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<div class="line"><span class="lineno"> 67</span>}</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<p >main function </p>
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<div class="fragment"><div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> {</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"expected value : "</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"variance : "</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"standard deviation : "</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> </div>
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<div class="line"><a id="l00093" name="l00093"></a><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> << <span class="stringliteral">"exactly 30 successes : "</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
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||||
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</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="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"45 or more successes : "</span></div>
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||||
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span>}</div>
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<div class="fragment"><div class="line"><span class="lineno"> 84</span> {</div>
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<div class="line"><span class="lineno"> 85</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"expected value : "</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a>(100, 0.5)</div>
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||||
<div class="line"><span class="lineno"> 86</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 87</span> </div>
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<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"variance : "</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#acd4dd4558031e4c5d045c801f73d8861">binomial_variance</a>(100, 0.5) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 89</span> </div>
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<div class="line"><span class="lineno"> 90</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"standard deviation : "</span></div>
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||||
<div class="line"><span class="lineno"> 91</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#af09e51f513cee647d41192ab0a872cdc">binomial_standard_deviation</a>(100, 0.5) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 92</span> </div>
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<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> << <span class="stringliteral">"exactly 30 successes : "</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a>(100, 0.5, 30)</div>
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||||
<div class="line"><span class="lineno"> 94</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 95</span> </div>
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<div class="line"><span class="lineno"> 96</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"45 or more successes : "</span></div>
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<div class="line"><span class="lineno"> 97</span> << <a class="code hl_function" href="../../d6/db0/binomial__dist_8cpp.html#a76ed6ce71415fb400b65f0656cef3d25">binomial_range_successes</a>(100, 0.5, 45, 100) << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 98</span> </div>
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<div class="line"><span class="lineno"> 99</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 100</span>}</div>
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<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>
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||||
<div class="ttc" id="abinomial__dist_8cpp_html_a19ae0a6a2bd200fd1eb0e31b2bf4cc76"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a19ae0a6a2bd200fd1eb0e31b2bf4cc76">binomial_x_successes</a></div><div class="ttdeci">double binomial_x_successes(double n, double p, double x)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:65</div></div>
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<div class="ttc" id="abinomial__dist_8cpp_html_a4416a7bc7fa87201883c54cdc4c82813"><div class="ttname"><a href="../../d6/db0/binomial__dist_8cpp.html#a4416a7bc7fa87201883c54cdc4c82813">binomial_expected</a></div><div class="ttdeci">double binomial_expected(double n, double p)</div><div class="ttdef"><b>Definition:</b> binomial_dist.cpp:22</div></div>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>\(\displaystyle {n\choose r} = \frac{n!}{r!(n-r)!} = \frac{n\times(n-1)\times(n-2)\times\cdots(n-r)}{r!} \) </dd></dl>
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<div class="fragment"><div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> {</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordtype">double</span> numerator = n;</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordtype">double</span> denominator = r;</div>
|
||||
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> </div>
|
||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i >= ((n - r) + 1); i--) {</div>
|
||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> numerator *= i;</div>
|
||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> }</div>
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i < r; i++) {</div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> denominator *= i;</div>
|
||||
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> }</div>
|
||||
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> </div>
|
||||
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="keywordflow">return</span> numerator / denominator;</div>
|
||||
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span>}</div>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 47</span> {</div>
|
||||
<div class="line"><span class="lineno"> 48</span> <span class="keywordtype">double</span> numerator = n;</div>
|
||||
<div class="line"><span class="lineno"> 49</span> <span class="keywordtype">double</span> denominator = r;</div>
|
||||
<div class="line"><span class="lineno"> 50</span> </div>
|
||||
<div class="line"><span class="lineno"> 51</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = n - 1; i >= ((n - r) + 1); i--) {</div>
|
||||
<div class="line"><span class="lineno"> 52</span> numerator *= i;</div>
|
||||
<div class="line"><span class="lineno"> 53</span> }</div>
|
||||
<div class="line"><span class="lineno"> 54</span> </div>
|
||||
<div class="line"><span class="lineno"> 55</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i < r; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 56</span> denominator *= i;</div>
|
||||
<div class="line"><span class="lineno"> 57</span> }</div>
|
||||
<div class="line"><span class="lineno"> 58</span> </div>
|
||||
<div class="line"><span class="lineno"> 59</span> <span class="keywordflow">return</span> numerator / denominator;</div>
|
||||
<div class="line"><span class="lineno"> 60</span>}</div>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
||||
</div>
|
||||
@@ -460,7 +460,7 @@ Here is the call graph for this function:</div>
|
||||
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