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| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg"></a><a class="link" href="dist_construct_eg.html" title="Distribution Construction Example"> |
| Distribution Construction Example</a> |
| </h5></div></div></div> |
| <p> |
| See <a href="../../../../../../../example/distribution_construction.cpp" target="_top">distribution_construction.cpp</a> |
| for full source code. |
| </p> |
| <p> |
| </p> |
| <p> |
| The structure of distributions is rather different from some other |
| statistical libraries, for example in less object-oriented language |
| like FORTRAN and C, that provide a few arguments to each free function. |
| This library provides each distribution as a template C++ class. A |
| distribution is constructed with a few arguments, and then member and |
| non-member functions are used to find values of the distribution, often |
| a function of a random variate. |
| </p> |
| <p> |
| </p> |
| <p> |
| First we need some includes to access the negative binomial distribution |
| (and the binomial, beta and gamma too). |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">negative_binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for negative_binomial_distribution |
| </span> <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span> <span class="comment">// default type is double. |
| </span> <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span> <span class="comment">// typedef provides default type is double. |
| </span><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">binomial</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for binomial_distribution. |
| </span><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">beta</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for beta_distribution. |
| </span><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for gamma_distribution. |
| </span><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> <span class="comment">// for normal_distribution.</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Several examples of constructing distributions follow: |
| </p> |
| <p> |
| </p> |
| <p> |
| First, a negative binomial distribution with 8 successes and a success |
| fraction 0.25, 25% or 1 in 4, is constructed like this: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">mydist0</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| But this is inconveniently long, so we might be tempted to write |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| but this might risk ambiguity with names in std random so *much better |
| is explicit <code class="computeroutput"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span> </code> * ... statements like |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial_distribution</span><span class="special">;</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| and we can still reduce typing. |
| </p> |
| <p> |
| </p> |
| <p> |
| Since the vast majority of applications use will be using double precision, |
| the template argument to the distribution (RealType) defaults to type |
| double, so we can also write: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special"><></span> <span class="identifier">mydist9</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> <span class="comment">// Uses default RealType = double.</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| But the name "negative_binomial_distribution" is still inconveniently |
| long, so for most distributions, a convenience typedef is provided, |
| for example: |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">negative_binomial</span><span class="special">;</span> <span class="comment">// Reserved name of type double. |
| </span></pre> |
| <p> |
| </p> |
| <div class="caution"><table border="0" summary="Caution"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/src/images/caution.png"></td> |
| <th align="left">Caution</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| This convenience typedef is <span class="emphasis"><em>not</em></span> provided if |
| a clash would occur with the name of a function: currently only "beta" |
| and "gamma" fall into this category. |
| </p></td></tr> |
| </table></div> |
| <p> |
| </p> |
| <p> |
| So, after a using statement, |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">negative_binomial</span><span class="special">;</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| we have a convenient typedef to <code class="computeroutput"><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Some more examples using the convenience typedef: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist10</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Both arguments double.</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| And automatic conversion takes place, so you can use integers and floats: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist11</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Using provided typedef double, int and double arguments.</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| This is probably the most common usage. |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial</span> <span class="identifier">mydist12</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="number">0.4F</span><span class="special">);</span> <span class="comment">// Double and float arguments. |
| </span><span class="identifier">negative_binomial</span> <span class="identifier">mydist13</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Both arguments integer.</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| Similarly for most other distributions like the binomial. |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">binomial</span> <span class="identifier">mybinomial</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// is more concise than |
| </span><span class="identifier">binomial_distribution</span><span class="special"><></span> <span class="identifier">mybinomd1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| For cases when the typdef distribution name would clash with a math |
| special function (currently only beta and gamma) the typedef is deliberately |
| not provided, and the longer version of the name must be used. For |
| example do not use: |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta</span><span class="special">;</span> |
| <span class="identifier">beta</span> <span class="identifier">mybetad0</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// Error beta is a math FUNCTION! |
| </span></pre> |
| <p> |
| </p> |
| <p> |
| Which produces the error messages: |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting">error C2146: syntax error : missing ';' before identifier 'mybetad0' |
| warning C4551: function call missing argument list |
| error C3861: 'mybetad0': identifier not found |
| </pre> |
| <p> |
| </p> |
| <p> |
| Instead you should use: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta_distribution</span><span class="special">;</span> |
| <span class="identifier">beta_distribution</span><span class="special"><></span> <span class="identifier">mybetad1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| or for the gamma distribution: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">gamma_distribution</span><span class="special"><></span> <span class="identifier">mygammad1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| We can, of course, still provide the type explicitly thus: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="comment">// Explicit double precision: |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">mydist1</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> |
| |
| <span class="comment">// Explicit float precision, double arguments are truncated to float: |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">mydist2</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> |
| |
| <span class="comment">// Explicit float precision, integer & double arguments converted to float. |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">mydist3</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> |
| |
| <span class="comment">// Explicit float precision, float arguments, so no conversion: |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">mydist4</span><span class="special">(</span><span class="number">8.F</span><span class="special">,</span> <span class="number">0.25F</span><span class="special">);</span> |
| |
| <span class="comment">// Explicit float precision, integer arguments promoted to float. |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">mydist5</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| |
| <span class="comment">// Explicit double precision: |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">mydist6</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span> |
| |
| <span class="comment">// Explicit long double precision: |
| </span><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">mydist7</span><span class="special">(</span><span class="number">8.</span><span class="special">,</span> <span class="number">0.25</span><span class="special">);</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| And if you have your own RealType called MyFPType, for example NTL |
| RR (an arbitrary precision type), then we can write: |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special"><</span><span class="identifier">MyFPType</span><span class="special">></span> <span class="identifier">mydist6</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// Integer arguments -> MyFPType. |
| </span></pre> |
| <p> |
| <a name="math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_"></a> |
| </p> |
| <h6> |
| <a name="id927637"></a> |
| <a class="link" href="dist_construct_eg.html#math_toolkit.dist.stat_tut.weg.dist_construct_eg.default_arguments_to_distribution_constructors_">Default |
| arguments to distribution constructors.</a> |
| </h6> |
| <p> |
| </p> |
| <p> |
| Note that default constructor arguments are only provided for some |
| distributions. So if you wrongly assume a default argument you will |
| get an error message, for example: |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special"><></span> <span class="identifier">mydist8</span><span class="special">;</span> |
| </pre> |
| <p> |
| |
| </p> |
| <pre class="programlisting">error C2512 no appropriate default constructor available.</pre> |
| <p> |
| </p> |
| <p> |
| No default constructors are provided for the negative binomial, because |
| it is difficult to chose any sensible default values for this distribution. |
| For other distributions, like the normal distribution, it is obviously |
| very useful to provide 'standard' defaults for the mean and standard |
| deviation thus: |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">normal_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">sd</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| So in this case we can write: |
| </p> |
| <p> |
| </p> |
| <p> |
| |
| </p> |
| <pre class="programlisting"> <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal</span><span class="special">;</span> |
| |
| <span class="identifier">normal</span> <span class="identifier">norm1</span><span class="special">;</span> <span class="comment">// Standard normal distribution. |
| </span> <span class="identifier">normal</span> <span class="identifier">norm2</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> <span class="comment">// Mean = 2, std deviation = 1. |
| </span> <span class="identifier">normal</span> <span class="identifier">norm3</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Mean = 2, std deviation = 3. |
| </span> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> <span class="comment">// int main()</span></pre> |
| <p> |
| </p> |
| <p> |
| </p> |
| <p> |
| There is no useful output from this program, of course. |
| </p> |
| <p> |
| </p> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 John Maddock, Paul A. Bristow, |
| Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and |
| Thijs van den Berg<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
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