File: future.html

package info (click to toggle)
boost1.35 1.35.0-5
  • links: PTS
  • area: main
  • in suites: lenny
  • size: 203,856 kB
  • ctags: 337,867
  • sloc: cpp: 938,683; xml: 56,847; ansic: 41,589; python: 18,999; sh: 11,566; makefile: 664; perl: 494; yacc: 456; asm: 353; csh: 6
file content (141 lines) | stat: -rw-r--r-- 11,905 bytes parent folder | download 
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
 
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Extras/Future Directions</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" 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/people/people.htm">People</a></td>
<td align="center"><a href="http://www.boost.org/more/faq.htm">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/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../../../../doc/html/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 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="id616918"></a>
        <a 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">&lt;</span><span class="keyword">class</span> <span class="identifier">Dist</span><span class="special">&gt;</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="id617145"></a>
        <a 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">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">&gt;</span>
   <span class="identifier">any_distribution</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Distribution</span><span class="special">&amp;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</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">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;&amp;</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="id617442"></a>
        <a 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">&lt;</span><span class="keyword">class</span> <span class="identifier">InputIterator</span><span class="special">&gt;</span>
<span class="keyword">typename</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">iterator_traits</span><span class="special">&lt;</span><span class="identifier">InputIterator</span><span class="special">&gt;::</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">&lt;</span><span class="identifier">InputIterator</span><span class="special">&gt;::</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="id617674"></a>
        <a 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">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special">&lt;</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">test_expected_mean</span><span class="special">&gt;</span> <span class="special">&gt;</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 John Maddock, Paul A. Bristow, Hubert Holin
      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></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
</body>
</html>