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  <refnamediv>
    <refname>distfun_nctstat</refname>
    <refpurpose>Noncentral T  mean and variance</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   M = distfun_nctstat ( v , delta )
   [M,V] = distfun_nctstat ( v , delta )
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
   <varlistentry><term>v :</term>
      <listitem><para> a matrix of doubles, the number of degrees of freedom, v>0.</para></listitem></varlistentry>
   <varlistentry><term>delta :</term>
      <listitem><para> a matrix of doubles, the noncentrality parameter, delta is real</para></listitem></varlistentry>
   <varlistentry><term>M :</term>
      <listitem><para> a matrix of doubles, the mean</para></listitem></varlistentry>
   <varlistentry><term>V :</term>
      <listitem><para> a matrix of doubles, the variance</para></listitem></varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
Computes statistics from the Noncentral T distribution.
   </para>
   <para>
The mean of the Noncentral T distribution is
   </para>
   <para>
<latex>
\begin{eqnarray}
M=\delta \sqrt{v/2} \frac{\Gamma((v-1)/2)}{\Gamma(v/2)}
\end{eqnarray}
</latex>
   </para>
   <para>
if v &gt; 1. M is undefined if 0 &lt; v &lt;= 1.
   </para>
   <para>
The variance of the Noncentral T distribution is
   </para>
   <para>
<latex>
\begin{eqnarray}
V=\frac{v(1+\delta^2)}{v-2} - M^2
\end{eqnarray}
</latex>
   </para>
   <para>
if v &gt; 2.
V is undefined if 0 &lt; v &lt;= 2.
   </para>
   <para>
Any scalar input argument is expanded to a matrix of
doubles of the same size as the other input arguments.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
delta=10;
v = [0.5 1 1.5 2 2.3 4];
[M,V]=distfun_nctstat(v,delta)
me=[%nan %nan %nan %nan 521.0145  44.920367]
ve=[%nan %nan 25.622878  17.724539  15.915993  12.533141]

   ]]></programlisting>
</refsection>

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