\section{RANDF Generate F-Distributed Random Variable}

\subsection{Usage}

Generates random variables with an F-distribution.  The general
syntax for its use is
\begin{verbatim}
   y = randf(n,m)
\end{verbatim}
where \verb|n| and \verb|m| are vectors of the number of degrees of freedom
in the numerator and denominator of the chi-square random variables
whose ratio defines the statistic.
\subsection{Function Internals}

The statistic \verb|F_{n,m}| is defined as the ratio of two chi-square
random variables:
\[
  F_{n,m} = \frac{\chi_n^2/n}{\chi_m^2/m}
\]
The PDF is given by
\[
  f_{n,m} = \frac{m^{m/2}n^{n/2}x^{n/2-1}}{(m+nx)^{(n+m)/2}B(n/2,m/2)},
\]
where \verb|B(a,b)| is the beta function.
\subsection{Example}

Here we use \verb|randf| to generate some F-distributed random variables,
and then again using the \verb|randchi| function:
\begin{verbatim}
--> randf(5*ones(1,9),7)
ans = 
  <float>  - size: [1 9]
 
Columns 1 to 6
 1.194351196  0.906920850  0.755768538  1.502930284  0.062067628  1.386031985  
 
Columns 7 to 9
 1.816088676  0.375541776  3.579419374  
--> randchi(5*ones(1,9))./randchi(7*ones(1,9))
ans = 
  <float>  - size: [1 9]
 
Columns 1 to 7
 1.3084840  1.2693102  1.0684280  0.4377135  1.1158004  0.7171145  0.4150873  
 
Columns 8 to 9
 1.8022333  1.4605886  

\end{verbatim}
