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<title>Comparison with C, R, FORTRAN-style Free Functions</title>
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<div class="titlepage"><div><div><h4 class="title">
<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
C, R, FORTRAN-style Free Functions</a>
</h4></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">&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>
</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">&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>
<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>
<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>
<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>
<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>
</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 &lt;= 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 &gt; 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>
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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>)
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