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| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="math_toolkit.dist.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects"> Distributions |
| are Objects</a> |
| </h5></div></div></div> |
| <p> |
| Each kind of distribution in this library is a class type - an object. |
| </p> |
| <p> |
| <a class="link" href="../../../policy.html" title="Policies">Policies</a> provide fine-grained |
| control of the behaviour of these classes, allowing the user to customise |
| behaviour such as how errors are handled, or how the quantiles of discrete |
| distribtions behave. |
| </p> |
| <div class="tip"><table border="0" summary="Tip"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../../../doc/src/images/tip.png"></td> |
| <th align="left">Tip</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| If you are familiar with statistics libraries using functions, and |
| 'Distributions as Objects' seem alien, see <a class="link" href="../weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">the |
| comparison to other statistics libraries.</a> |
| </p></td></tr> |
| </table></div> |
| <p> |
| Making distributions class types does two things: |
| </p> |
| <div class="itemizedlist"><ul type="disc"> |
| <li> |
| It encapsulates the kind of distribution in the C++ type system; |
| so, for example, Students-t distributions are always a different |
| C++ type from Chi-Squared distributions. |
| </li> |
| <li> |
| The distribution objects store any parameters associated with the |
| distribution: for example, the Students-t distribution has a <span class="emphasis"><em>degrees |
| of freedom</em></span> parameter that controls the shape of the distribution. |
| This <span class="emphasis"><em>degrees of freedom</em></span> parameter has to be |
| provided to the Students-t object when it is constructed. |
| </li> |
| </ul></div> |
| <p> |
| Although the distribution classes in this library are templates, there |
| are typedefs on type <span class="emphasis"><em>double</em></span> that mostly take the |
| usual name of the distribution (except where there is a clash with a |
| function of the same name: beta and gamma, in which case using the default |
| template arguments - <code class="computeroutput"><span class="identifier">RealType</span> |
| <span class="special">=</span> <span class="keyword">double</span></code> |
| - is nearly as convenient). Probably 95% of uses are covered by these |
| typedefs: |
| </p> |
| <pre class="programlisting"><span class="comment">// using namespace boost::math; // Avoid potential ambiguity with names in std <random> |
| </span><span class="comment">// Safer to declare specific functions with using statement(s): |
| </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">beta_distribution</span><span class="special">;</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">binomial_distribution</span><span class="special">;</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">students_t</span><span class="special">;</span> |
| |
| <span class="comment">// Construct a students_t distribution with 4 degrees of freedom: |
| </span><span class="identifier">students_t</span> <span class="identifier">d1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| |
| <span class="comment">// Construct a double-precision beta distribution |
| </span><span class="comment">// with parameters a = 10, b = 20 |
| </span><span class="identifier">beta_distribution</span><span class="special"><></span> <span class="identifier">d2</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> <span class="comment">// Note: _distribution<> suffix ! |
| </span></pre> |
| <p> |
| If you need to use the distributions with a type other than <code class="computeroutput"><span class="keyword">double</span></code>, then you can instantiate the template |
| directly: the names of the templates are the same as the <code class="computeroutput"><span class="keyword">double</span></code> typedef but with <code class="computeroutput"><span class="identifier">_distribution</span></code> appended, for example: |
| <a class="link" href="../../dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students |
| t Distribution</a> or <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial |
| Distribution</a>: |
| </p> |
| <pre class="programlisting"><span class="comment">// Construct a students_t distribution, of float type, |
| </span><span class="comment">// with 4 degrees of freedom: |
| </span><span class="identifier">students_t_distribution</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span> <span class="identifier">d3</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| |
| <span class="comment">// Construct a binomial distribution, of long double type, |
| </span><span class="comment">// with probability of success 0.3 |
| </span><span class="comment">// and 20 trials in total: |
| </span><span class="identifier">binomial_distribution</span><span class="special"><</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">d4</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">);</span> |
| </pre> |
| <p> |
| The parameters passed to the distributions can be accessed via getter |
| member functions: |
| </p> |
| <pre class="programlisting"><span class="identifier">d1</span><span class="special">.</span><span class="identifier">degrees_of_freedom</span><span class="special">();</span> <span class="comment">// returns 4.0 |
| </span></pre> |
| <p> |
| This is all well and good, but not very useful so far. What we often |
| want is to be able to calculate the <span class="emphasis"><em>cumulative distribution |
| functions</em></span> and <span class="emphasis"><em>quantiles</em></span> etc for these |
| distributions. |
| </p> |
| </div> |
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| <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>) |
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