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  <refnamediv>
    <refname>distfun_gamfitmm</refname>
    <refpurpose>Gamma parameter estimates with method of moments</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   parmhat = distfun_gamfitmm( data )
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
   <varlistentry><term>data :</term>
      <listitem><para> a matrix of doubles, the data, data>=0.</para></listitem></varlistentry>
   <varlistentry><term>parmhat :</term>
      <listitem><para> a 1-by-2 matrix of doubles, the parameters of the Gamma distribution. parmhat(1) is a, parmhat(2) is b.</para></listitem></varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
Estimates the parameters of the Gamma distribution
with method of moments.
In other words, finds the parameters so that
the mean and variance of the distribution are
equal to the empirical mean and empirical variance of the
data.
   </para>
   <para>
The implementation is based on direct inversion of the moments.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
// Samples from Gamma distribution with
// a=12 and b=42
data = [
547.53259
347.58207
539.14939
342.82908
508.80556
386.28445
420.16239
725.67277
409.08739
726.20491
]
parmhat = distfun_gamfitmm(data)
a=parmhat(1);
b=parmhat(2);
// Compare the (mean,variance) of the
// distribution against the data :
// must be equal.
[M,V]=distfun_gamstat(a,b)
M_data=mean(data)
V_data=variance(data)

   ]]></programlisting>
</refsection>

<refsection>
   <title>Authors</title>
   <simplelist type="vert">
   <member>Copyright (C) 2014 - Michael Baudin</member>
   </simplelist>
</refsection>
</refentry>
