1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Extras/Future Directions</title> 5<link rel="stylesheet" href="../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../dist.html" title="Chapter 5. Statistical Distributions and Functions"> 9<link rel="prev" href="dist_ref/dist_algorithms.html" title="Distribution Algorithms"> 10<link rel="next" href="../statistics.html" title="Chapter 6. Statistics"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<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="../statistics.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 27<a name="math_toolkit.future"></a><a class="link" href="future.html" title="Extras/Future Directions">Extras/Future Directions</a> 28</h2></div></div></div> 29<h5> 30<a name="math_toolkit.future.h0"></a> 31 <span class="phrase"><a name="math_toolkit.future.adding_additional_location_and_s"></a></span><a class="link" href="future.html#math_toolkit.future.adding_additional_location_and_s">Adding 32 Additional Location and Scale Parameters</a> 33 </h5> 34<p> 35 In some modelling applications we require a distribution with a specific location 36 and scale: often this equates to a specific mean and standard deviation, although 37 for many distributions the relationship between these properties and the location 38 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> 39 for more information. 40 </p> 41<p> 42 The obvious way to handle this is via an adapter template: 43 </p> 44<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> 45<span class="keyword">class</span> <span class="identifier">scaled_distribution</span> 46<span class="special">{</span> 47 <span class="identifier">scaled_distribution</span><span class="special">(</span> 48 <span class="keyword">const</span> <span class="identifier">Dist</span> <span class="identifier">dist</span><span class="special">,</span> 49 <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> 50 <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> 51<span class="special">};</span> 52</pre> 53<p> 54 Which would then have its own set of overloads for the non-member accessor 55 functions. 56 </p> 57<h5> 58<a name="math_toolkit.future.h1"></a> 59 <span class="phrase"><a name="math_toolkit.future.an_any_distribution_class"></a></span><a class="link" href="future.html#math_toolkit.future.an_any_distribution_class">An 60 "any_distribution" class</a> 61 </h5> 62<p> 63 It is easy to add a distribution object that virtualises the actual type of 64 the distribution, and can therefore hold "any" object that conforms 65 to the conceptual requirements of a distribution: 66 </p> 67<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> 68<span class="keyword">class</span> <span class="identifier">any_distribution</span> 69<span class="special">{</span> 70<span class="keyword">public</span><span class="special">:</span> 71 <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">></span> 72 <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> 73<span class="special">};</span> 74 75<span class="comment">// Get the cdf of the underlying distribution:</span> 76<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">></span> 77<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> 78<span class="comment">// etc....</span> 79</pre> 80<p> 81 Such a class would facilitate the writing of non-template code that can function 82 with any distribution type. 83 </p> 84<p> 85 The <a href="http://sourceforge.net/projects/distexplorer/" target="_top">Statistical 86 Distribution Explorer</a> utility for Windows is a usage example. 87 </p> 88<p> 89 It's not clear yet whether there is a compelling use case though. Possibly 90 tests for goodness of fit might provide such a use case: this needs more investigation. 91 </p> 92<h5> 93<a name="math_toolkit.future.h2"></a> 94 <span class="phrase"><a name="math_toolkit.future.higher_level_hypothesis_tests"></a></span><a class="link" href="future.html#math_toolkit.future.higher_level_hypothesis_tests">Higher 95 Level Hypothesis Tests</a> 96 </h5> 97<p> 98 Higher-level tests roughly corresponding to the <a href="http://documents.wolfram.com/mathematica/Add-onsLinks/StandardPackages/Statistics/HypothesisTests.html" target="_top">Mathematica 99 Hypothesis Tests</a> package could be added reasonably easily, for example: 100 </p> 101<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> 102<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> 103 <span class="identifier">test_equal_mean</span><span class="special">(</span> 104 <span class="identifier">InputIterator</span> <span class="identifier">a</span><span class="special">,</span> 105 <span class="identifier">InputIterator</span> <span class="identifier">b</span><span class="special">,</span> 106 <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> 107</pre> 108<p> 109 Returns the probability that the data in the sequence [a,b) has the mean <span class="emphasis"><em>expected_mean</em></span>. 110 </p> 111<h5> 112<a name="math_toolkit.future.h3"></a> 113 <span class="phrase"><a name="math_toolkit.future.integration_with_statistical_acc"></a></span><a class="link" href="future.html#math_toolkit.future.integration_with_statistical_acc">Integration 114 With Statistical Accumulators</a> 115 </h5> 116<p> 117 <a href="http://boost-sandbox.sourceforge.net/libs/accumulators/doc/html/index.html" target="_top">Eric 118 Niebler's accumulator framework</a> - also work in progress - provides 119 the means to calculate various statistical properties from experimental data. 120 There is an opportunity to integrate the statistical tests with this framework 121 at some later date: 122 </p> 123<pre class="programlisting"><span class="comment">// Define an accumulator, all required statistics to calculate the test</span> 124<span class="comment">// are calculated automatically:</span> 125<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> 126<span class="comment">// Pass our data to the accumulator:</span> 127<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> 128<span class="comment">// Extract the result:</span> 129<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> 130</pre> 131</div> 132<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 133<td align="left"></td> 134<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 135 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 136 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 137 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 138 Daryle Walker and Xiaogang Zhang<p> 139 Distributed under the Boost Software License, Version 1.0. (See accompanying 140 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>) 141 </p> 142</div></td> 143</tr></table> 144<hr> 145<div class="spirit-nav"> 146<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="../statistics.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 147</div> 148</body> 149</html> 150
