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  <refnamediv>
    <refname>distfun_wblfitmm</refname>
    <refpurpose>Weibull parameter estimates with method of moments</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   parmhat = distfun_wblfitmm( 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 Weibull distribution. parmhat(1) is a, parmhat(2) is b.</para></listitem></varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
Estimates the parameters of the Weibull 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 the fact that the
coefficient of variation of the Weibull distribution
only depends on b.
The algorithm first searches for b, using a
zero solver.
Then the parameter a is computed depending on b.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
// Samples from Weibull distribution with
// a=5432 and b=3.21
data = [
3303.
3172.
2473.
5602.
3109.
4415.
6471.
5952.
3945.
3534.
]
parmhat = distfun_wblfitmm(data)
a=parmhat(1);
b=parmhat(2);
// Compare the (mean,variance) of the
// distribution against the data :
// must be equal.
[M,V]=distfun_wblstat(a,b)
M_data=mean(data)
V_data=variance(data)

   ]]></programlisting>
</refsection>

<refsection>
   <title>Authors</title>
   <simplelist type="vert">
   <member>Copyright (C) 2012 - 2014 - Michael Baudin</member>
   </simplelist>
</refsection>
</refentry>
