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| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="math_toolkit.dist.stat_tut.weg.nag_library"></a><a class="link" href="nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions"> Comparison |
| with C, R, FORTRAN-style Free Functions</a> |
| </h5></div></div></div> |
| <p> |
| You are probably familiar with a statistics library that has free functions, |
| for example the classic <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG |
| C library</a> and matching <a href="http://nag.com/numeric/FL/FLdescription.asp" target="_top">NAG |
| FORTRAN Library</a>, <a href="http://office.microsoft.com/en-us/excel/HP052090051033.aspx" target="_top">Microsoft |
| 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 |
| pbinom</a> and many others. |
| </p> |
| <p> |
| If so, you may find 'Distributions as Objects' unfamiliar, if not alien. |
| </p> |
| <p> |
| However, <span class="bold"><strong>do not panic</strong></span>, both definition |
| and usage are not really very different. |
| </p> |
| <p> |
| A very simple example of generating the same values as the <a href="http://nag.com/numeric/CL/CLdescription.asp" target="_top">NAG |
| C library</a> for the binomial distribution follows. (If you find |
| slightly different values, the Boost C++ version, using double or better, |
| is very likely to be the more accurate. Of course, accuracy is not usually |
| a concern for most applications of this function). |
| </p> |
| <p> |
| The <a href="http://www.nag.co.uk/numeric/cl/manual/pdf/G01/g01bjc.pdf" target="_top">NAG |
| function specification</a> is |
| </p> |
| <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> |
| <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> |
| </pre> |
| <p> |
| and is called |
| </p> |
| <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> |
| </pre> |
| <p> |
| The equivalent using this Boost C++ library is: |
| </p> |
| <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><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></pre> |
| <p> |
| and values can be output thus: |
| </p> |
| <pre class="programlisting"><span class="identifier">cout</span> |
| <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> <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> <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> <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> <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></pre> |
| <p> |
| <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 equivalent to NAG library <code class="computeroutput"><span class="identifier">plek</span></code>, |
| lower tail probability of <= k |
| </p> |
| <p> |
| <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 equivalent to NAG library <code class="computeroutput"><span class="identifier">pgtk</span></code>, |
| upper tail probability of > k |
| </p> |
| <p> |
| <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 equivalent to NAG library <code class="computeroutput"><span class="identifier">peqk</span></code>, |
| point probability of == k |
| </p> |
| <p> |
| See <a href="../../../../../../../example/binomial_example_nag.cpp" target="_top">binomial_example_nag.cpp</a> |
| for details. |
| </p> |
| </div> |
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| 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>) |
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