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  <refnamediv>
    <refname>distfun_ncfcdf</refname>
    <refpurpose>Noncentral F CDF</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   p = distfun_ncfcdf(x,v1,v2,delta)
   p = distfun_ncfcdf(x,v1,v2,delta,lowertail)
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
   <varlistentry><term>x :</term>
      <listitem><para> a matrix of doubles. x is real and x>=0.</para></listitem></varlistentry>
   <varlistentry><term>v1 :</term>
      <listitem><para> a matrix of doubles, numerator degrees of freedom, v1&gt;0 (can be non integer).</para></listitem></varlistentry>
   <varlistentry><term>v2 :</term>
      <listitem><para> a matrix of doubles, denominator degrees of freedom, v2&gt;0 (can be non integer).</para></listitem></varlistentry>
   <varlistentry><term>delta :</term>
      <listitem><para> a matrix of doubles, the noncentrality parameter, delta>=0</para></listitem></varlistentry>
   <varlistentry><term>lowertail :</term>
      <listitem><para> a 1-by-1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then considers P(X&lt;=x) otherwise P(X&gt;x).</para></listitem></varlistentry>
   <varlistentry><term>p :</term>
      <listitem><para> a matrix of doubles, the probability.</para></listitem></varlistentry>
   </variablelist>
</refsection>

<refsection>
   <title>Description</title>
   <para>
Computes the cumulative distribution function of
the Noncentral F distribution function.
   </para>
   <para>
Any scalar input argument is expanded to a matrix of doubles
of the same size as the other input arguments.
   </para>
   <para>
<emphasis>Caution</emphasis>
This distribution is known to have inferior accuracy in
some cases.
   </para>
   <para>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
// Test with x, v1, v2 scalar
computed = distfun_ncfcdf(5,4,12,0.3)
expected = 0.98319765219863320

// Plot the function
h=scf();
x = linspace(0,15,1000);
p1 = distfun_ncfcdf(x,10,20,0);
p2 = distfun_ncfcdf(x,10,20,1);
p3 = distfun_ncfcdf(x,10,20,5);
p4 = distfun_ncfcdf(x,10,20,10);
p5 = distfun_ncfcdf(x,10,20,40);
plot(x,p1,"r")
plot(x,p2,"g")
plot(x,p3,"b")
plot(x,p4,"y")
plot(x,p5,"k")
legend([
"v1=10, v2=20, delta=0"
"v1=10, v2=20, delta=1"
"v1=10, v2=20, delta=5"
"v1=10, v2=20, delta=10"
"v1=10, v2=20, delta=40"
]);
xtitle("Noncentral F CDF","x","$P(X\leq x)$");

   ]]></programlisting>
</refsection>

<refsection>
   <title>Bibliography</title>
   <para>http://en.wikipedia.org/wiki/Noncentral_F-distribution</para>
   <para>http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/dist_ref/dists/nc_f_dist.html</para>
</refsection>

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