1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
|
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Extras/Future Directions</title>
<link rel="stylesheet" href="../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Math Toolkit 4.2.1">
<link rel="up" href="../dist.html" title="Chapter 5. Statistical Distributions and Functions">
<link rel="prev" href="dist_ref/dist_algorithms.html" title="Distribution Algorithms">
<link rel="next" href="../statistics.html" title="Chapter 6. Statistics">
<meta name="viewport" content="width=device-width, initial-scale=1">
</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="../statistics.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.future"></a><a class="link" href="future.html" title="Extras/Future Directions">Extras/Future Directions</a>
</h2></div></div></div>
<h5>
<a name="math_toolkit.future.h0"></a>
<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
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>
<h5>
<a name="math_toolkit.future.h1"></a>
<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
"any_distribution" class</a>
</h5>
<p>
It is easy 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.
</p>
<p>
The <a href="http://sourceforge.net/projects/distexplorer/" target="_top">Statistical
Distribution Explorer</a> utility for Windows is a usage example.
</p>
<p>
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>
<h5>
<a name="math_toolkit.future.h2"></a>
<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
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>
<h5>
<a name="math_toolkit.future.h3"></a>
<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
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>
<div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<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>
<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="../statistics.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
|
