| <html> |
| <head> |
| <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> |
| <title>Extras/Future Directions</title> |
| <link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> |
| <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> |
| <link rel="home" href="../../index.html" title="Math Toolkit"> |
| <link rel="up" href="../dist.html" title="Statistical Distributions and Functions"> |
| <link rel="prev" href="dist_ref/dist_algorithms.html" title="Distribution Algorithms"> |
| <link rel="next" href="../special.html" title="Special Functions"> |
| </head> |
| <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> |
| <table cellpadding="2" width="100%"><tr> |
| <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td> |
| <td align="center"><a href="../../../../../../../index.html">Home</a></td> |
| <td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> |
| <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> |
| <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> |
| <td align="center"><a href="../../../../../../../more/index.htm">More</a></td> |
| </tr></table> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| <div class="section" lang="en"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.dist.future"></a><a class="link" href="future.html" title="Extras/Future Directions"> Extras/Future Directions</a> |
| </h3></div></div></div> |
| <a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters"></a><h5> |
| <a name="id1065718"></a> |
| <a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">Adding |
| Additional Location and Scale Parameters</a> |
| </h5> |
| <p> |
| In some modelling applications we require a distribution with a specific |
| location and scale: often this equates to a specific mean and standard deviation, |
| although for many distributions the relationship between these properties |
| and the location and scale parameters are non-trivial. See <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm" target="_top">http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm</a> |
| for more information. |
| </p> |
| <p> |
| The obvious way to handle this is via an adapter template: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">scaled_distribution</span> |
| <span class="special">{</span> |
| <span class="identifier">scaled_distribution</span><span class="special">(</span> |
| <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><span class="special">,</span> |
| <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">location</span><span class="special">,</span> |
| <span class="keyword">typename</span> <span class="identifier">Dist</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">scale</span> <span class="special">=</span> <span class="number">0</span><span class="special">);</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| Which would then have its own set of overloads for the non-member accessor |
| functions. |
| </p> |
| <a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a><h5> |
| <a name="id1065882"></a> |
| <a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An |
| "any_distribution" class</a> |
| </h5> |
| <p> |
| It would be fairly trivial to add a distribution object that virtualises |
| the actual type of the distribution, and can therefore hold "any" |
| object that conforms to the conceptual requirements of a distribution: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">any_distribution</span> |
| <span class="special">{</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">></span> |
| <span class="identifier">any_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Distribution</span><span class="special">&</span> <span class="identifier">d</span><span class="special">);</span> |
| <span class="special">};</span> |
| |
| <span class="comment">// Get the cdf of the underlying distribution: |
| </span><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span> |
| <span class="identifier">RealType</span> <span class="identifier">cdf</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">any_distribution</span><span class="special"><</span><span class="identifier">RealType</span><span class="special">>&</span> <span class="identifier">d</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">x</span><span class="special">);</span> |
| <span class="comment">// etc.... |
| </span></pre> |
| <p> |
| Such a class would facilitate the writing of non-template code that can function |
| with any distribution type. It's not clear yet whether there is a compelling |
| use case though. Possibly tests for goodness of fit might provide such a |
| use case: this needs more investigation. |
| </p> |
| <a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a><h5> |
| <a name="id1066091"></a> |
| <a class="link" href="future.html#math_toolkit.dist.future.higher_level_hypothesis_tests">Higher |
| Level Hypothesis Tests</a> |
| </h5> |
| <p> |
| Higher-level tests roughly corresponding to the <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html" target="_top">Mathematica |
| Hypothesis Tests</a> package could be added reasonably easily, for example: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">InputIterator</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">InputIterator</span><span class="special">>::</span><span class="identifier">value_type</span> |
| <span class="identifier">test_equal_mean</span><span class="special">(</span> |
| <span class="identifier">InputIterator</span> <span class="identifier">a</span><span class="special">,</span> |
| <span class="identifier">InputIterator</span> <span class="identifier">b</span><span class="special">,</span> |
| <span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special"><</span><span class="identifier">InputIterator</span><span class="special">>::</span><span class="identifier">value_type</span> <span class="identifier">expected_mean</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the probability that the data in the sequence [a,b) has the mean |
| <span class="emphasis"><em>expected_mean</em></span>. |
| </p> |
| <a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a><h5> |
| <a name="id1066253"></a> |
| <a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">Integration |
| With Statistical Accumulators</a> |
| </h5> |
| <p> |
| <a href="http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html" target="_top">Eric |
| Niebler's accumulator framework</a> - also work in progress - provides |
| the means to calculate various statistical properties from experimental data. |
| There is an opportunity to integrate the statistical tests with this framework |
| at some later date: |
| </p> |
| <pre class="programlisting"><span class="comment">// Define an accumulator, all required statistics to calculate the test |
| </span><span class="comment">// are calculated automatically: |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">test_expected_mean</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">expected_mean</span><span class="special">=</span><span class="number">4</span><span class="special">);</span> |
| <span class="comment">// Pass our data to the accumulator: |
| </span><span class="identifier">acc</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span><span class="identifier">mydata</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">mydata</span><span class="special">.</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">acc</span><span class="special">);</span> |
| <span class="comment">// Extract the result: |
| </span><span class="keyword">double</span> <span class="identifier">p</span> <span class="special">=</span> <span class="identifier">probability</span><span class="special">(</span><span class="identifier">acc</span><span class="special">);</span> |
| </pre> |
| </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> |
| <hr> |
| <div class="spirit-nav"> |
| <a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> |
| </div> |
| </body> |
| </html> |
