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  25 <div class="section math_toolkit_dist_stat_tut_weg_nag_library">
  26 <div class="titlepage"><div><div><h5 class="title">
  27 <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
  28           with C, R, FORTRAN-style Free Functions</a>
  29 </h5></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
  48             slightly different values, the Boost C++ version, using double or better,
  49             is very likely to be the more accurate. Of course, accuracy is not usually
  50             a concern 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">&amp;</span><span class="identifier">plek</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">pgtk</span><span class="special">,</span> <span class="special">&amp;</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">&lt;&lt;</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">trials</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span>             <span class="comment">// Echo the NAG input n = 4 trials.</span>
  75   <span class="special">&lt;&lt;</span> <span class="identifier">my_dist</span><span class="special">.</span><span class="identifier">success_fraction</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" "</span>   <span class="comment">// Echo the NAG input p = 0.5</span>
  76   <span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="string">"  "</span>             <span class="comment">// NAG plek with k = 2</span>
  77   <span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="string">"  "</span> <span class="comment">// NAG pgtk with k = 2</span>
  78   <span class="special">&lt;&lt;</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">&lt;&lt;</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>
  82             is equivalent to NAG library <code class="computeroutput"><span class="identifier">plek</span></code>,
  83             lower tail probability of &lt;= 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>
  87             is equivalent to NAG library <code class="computeroutput"><span class="identifier">pgtk</span></code>,
  88             upper tail probability of &gt; 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>
  92             is 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>
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 101 <td align="left"></td>
 102 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno
 103       Lalande, Johan R&#229;de, Gautam Sewani and Thijs van den Berg<p>
 104         Distributed under the Boost Software License, Version 1.0. (See accompanying
 105         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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