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  <refnamediv>
    <refname>distfun_evcdf</refname>
    <refpurpose>Extreme value (Gumbel) CDF</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   p=distfun_evcdf(x,mu,sigma)
   p=distfun_evcdf(x,mu,sigma,lowertail)
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
   <varlistentry><term>x :</term>
      <listitem><para> a matrix of doubles, the outcome</para></listitem></varlistentry>
   <varlistentry><term>mu :</term>
      <listitem><para> a matrix of doubles, the location</para></listitem></varlistentry>
   <varlistentry><term>sigma :</term>
      <listitem><para> a matrix of doubles, the scale. sigma>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 cumulated probability distribution function
of the Extreme value (Gumbel) function.
This is the minimum Gumbel distribution.
   </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[
// Test expanded arguments
computed = distfun_evcdf([1 2 3],1,2)
expected = [0.6321206 0.8077044 0.9340120]

// Plot the Gumbel CDF
N=1000;
x=linspace(-20,5,N);
p1= distfun_evcdf(x,-0.5,2.,%t);
p2= distfun_evcdf(x,-1.0,2.,%t);
p3= distfun_evcdf(x,-1.5,3.,%t);
p4= distfun_evcdf(x,-3.0,4.,%t);
scf();
xtitle("Gumbel","x","P(X<x)");
plot(x,p1,"r-")
plot(x,p2,"g-")
plot(x,p3,"b-")
plot(x,p4,"c-")
leg(1)="$\mu=-0.5,\beta=2.0$";
leg(2)="$\mu=-1.0,\beta=2.0$";
leg(3)="$\mu=-1.5,\beta=3.0$";
leg(4)="$\mu=-3.0,\beta=4.0$";
legend(leg,"in_upper_left");

p=distfun_evcdf(1,0.5,2.,%t)
q=distfun_evcdf(1,0.5,2.,%f)
p+q

   ]]></programlisting>
</refsection>

<refsection>
   <title>Authors</title>
   <simplelist type="vert">
   <member>Copyright (C) 2013 - Michael Baudin</member>
   </simplelist>
</refsection>
</refentry>
