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26 | <div class="titlepage"><div><div><h4 class="title"> | |
27 | <a name="math_toolkit.stat_tut.weg.nag_library"></a><a class="link" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">Comparison with | |
28 | C, R, FORTRAN-style Free Functions</a> | |
29 | </h4></div></div></div> | |
30 | <p> | |
31 | You are probably familiar with a statistics library that has free functions, | |
32 | for example the classic <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG | |
33 | C library</a> and matching <a href="http://nag.com/numeric/FL/FLdescription.asp" target="_top">NAG | |
34 | FORTRAN Library</a>, <a href="http://office.microsoft.com/en-us/excel/HP052090051033.aspx" target="_top">Microsoft | |
35 | Excel BINOMDIST(number_s,trials,probability_s,cumulative)</a>, <a href="http://www.r-project.org/" target="_top">R</a>, <a href="http://www.ptc.com/products/mathcad/mathcad14/mathcad_func_chart.htm" target="_top">MathCAD | |
36 | pbinom</a> and many others. | |
37 | </p> | |
38 | <p> | |
39 | If so, you may find 'Distributions as Objects' unfamiliar, if not alien. | |
40 | </p> | |
41 | <p> | |
42 | However, <span class="bold"><strong>do not panic</strong></span>, both definition | |
43 | and usage are not really very different. | |
44 | </p> | |
45 | <p> | |
46 | A very simple example of generating the same values as the <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG | |
47 | C library</a> for the binomial distribution follows. (If you find slightly | |
48 | different values, the Boost C++ version, using double or better, is very | |
49 | likely to be the more accurate. Of course, accuracy is not usually a concern | |
50 | for most applications of this function). | |
51 | </p> | |
52 | <p> | |
53 | The <a href="http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf" target="_top">NAG | |
54 | function specification</a> is | |
55 | </p> | |
56 | <pre class="programlisting"><span class="keyword">void</span> <span class="identifier">nag_binomial_dist</span><span class="special">(</span><span class="identifier">Integer</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">k</span><span class="special">,</span> | |
57 | <span class="keyword">double</span> <span class="special">*</span><span class="identifier">plek</span><span class="special">,</span> <span class="keyword">double</span> <span class="special">*</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="keyword">double</span> <span class="special">*</span><span class="identifier">peqk</span><span class="special">,</span> <span class="identifier">NagError</span> <span class="special">*</span><span class="identifier">fail</span><span class="special">)</span> | |
58 | </pre> | |
59 | <p> | |
60 | and is called | |
61 | </p> | |
62 | <pre class="programlisting"><span class="identifier">g01bjc</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">,</span> <span class="identifier">k</span><span class="special">,</span> <span class="special">&</span><span class="identifier">plek</span><span class="special">,</span> <span class="special">&</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="special">&</span><span class="identifier">peqk</span><span class="special">,</span> <span class="identifier">NAGERR_DEFAULT</span><span class="special">);</span> | |
63 | </pre> | |
64 | <p> | |
65 | The equivalent using this Boost C++ library is: | |
66 | </p> | |
67 | <pre class="programlisting"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">;</span> <span class="comment">// Using declaration avoids very long names.</span> | |
68 | <span class="identifier">binomial</span> <span class="identifier">my_dist</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="number">0.5</span><span class="special">);</span> <span class="comment">// c.f. NAG n = 4, p = 0.5</span> | |
69 | </pre> | |
70 | <p> | |
71 | and values can be output thus: | |
72 | </p> | |
73 | <pre class="programlisting"><span class="identifier">cout</span> | |
74 | <span class="special"><<</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" "</span> <span class="comment">// Echo the NAG input n = 4 trials.</span> | |
75 | <span class="special"><<</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special"><<</span> <span class="string">" "</span> <span class="comment">// Echo the NAG input p = 0.5</span> | |
76 | <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special"><<</span> <span class="string">" "</span> <span class="comment">// NAG plek with k = 2</span> | |
77 | <span class="special"><<</span> <span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">))</span> <span class="special"><<</span> <span class="string">" "</span> <span class="comment">// NAG pgtk with k = 2</span> | |
78 | <span class="special"><<</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">my_dist</span><span class="special">,</span> <span class="number">2</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// NAG peqk with k = 2</span> | |
79 | </pre> | |
80 | <p> | |
81 | <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">)</span></code> is | |
82 | equivalent to NAG library <code class="computeroutput"><span class="identifier">plek</span></code>, | |
83 | lower tail probability of <= k | |
84 | </p> | |
85 | <p> | |
86 | <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">))</span></code> is | |
87 | equivalent to NAG library <code class="computeroutput"><span class="identifier">pgtk</span></code>, | |
88 | upper tail probability of > k | |
89 | </p> | |
90 | <p> | |
91 | <code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">k</span><span class="special">)</span></code> is | |
92 | equivalent to NAG library <code class="computeroutput"><span class="identifier">peqk</span></code>, | |
93 | point probability of == k | |
94 | </p> | |
95 | <p> | |
96 | See <a href="../../../../../example/binomial_example_nag.cpp" target="_top">binomial_example_nag.cpp</a> | |
97 | for details. | |
98 | </p> | |
99 | </div> | |
100 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
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102 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
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105 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
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