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  <refnamediv>
    <refname>distfun_betacdf</refname>
    <refpurpose>Beta CDF</refpurpose>
  </refnamediv>


<refsynopsisdiv>
   <title>Calling Sequence</title>
   <synopsis>
   p = distfun_betacdf ( x , a , b )
   p = distfun_betacdf ( x , a , b , lowertail )
   
   </synopsis>
</refsynopsisdiv>

<refsection>
   <title>Parameters</title>
   <variablelist>
   <varlistentry><term>x :</term>
      <listitem><para> a matrix of doubles, the outcome. Should be in the [0,1] interval. If not, an error is generated.</para></listitem></varlistentry>
   <varlistentry><term>a :</term>
      <listitem><para> a matrix of doubles, the first shape parameter, a>=0.</para></listitem></varlistentry>
   <varlistentry><term>b :</term>
      <listitem><para> a matrix of doubles, the second shape parameter, b>=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 Beta cumulated 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>
</para>
</refsection>

<refsection>
   <title>Examples</title>
   <programlisting role="example"><![CDATA[
// Check expansion of a and b
computed = distfun_betacdf ( 0.1:0.2:0.9 , 2 , 2 )
expected = [0.0280,0.2160,0.5000,0.7840,0.9720]

// Check with expanded arguments
x = 0.1:0.2:0.9;
a = [2 3 4 5 6];
b = [5 4 3 2 1];
computed = distfun_betacdf ( x , a, b )
expected = [0.114265,0.25569,0.34375,0.420175,0.531441]

// Check bounds of x
// This generates an error:
// distfun_betacdf([-1 0 1 2],2,3)

// Plot the function
a = [0.5 5 1 2 2];
b = [0.5 1 3 2 5];
cols = [1 2 3 4 5];
nf = size(cols,"*");
lgd = [];
scf();
for k = 1 : nf
x = linspace(0,1,1000);
y = distfun_betacdf ( x , a(k) , b(k) );
plot(x,y)
str = msprintf("a=%s, b=%s",..
string(a(k)),string(b(k)));
lgd($+1) = str;
end
h = gcf();
for k = 1 : nf
hk = h.children.children.children(nf - k + 1);
hk.foreground = cols(k);
end
xtitle("Beta CDF","x","$P(X\leq x)$");
legend(lgd);

// See upper tail
p = distfun_betacdf ( 0.1:0.2:0.9 , 2 , 2 )
q = distfun_betacdf ( 0.1:0.2:0.9 , 2 , 2 , %f )
p+q
// See an extreme case
distfun_betacdf ( 0.999 , 1 , 10 , %f )
expected = 1.e-30

   ]]></programlisting>
</refsection>

<refsection>
   <title>Authors</title>
   <simplelist type="vert">
   <member>Copyright (C) 2012 - Michael Baudin</member>
   <member>Copyright (C) 2009-2011 - DIGITEO - Michael Baudin</member>
   </simplelist>
</refsection>
</refentry>
