function pdf=dfray(a, samples) 
% dfray(a, samples)  Generates a Rayleigh pdf with parameter a.  samples 
%    sets the size of the numerical representation, and is optional.  The 
%    default sample size is 1000. 
if nargin==1 
   samples=1000; 
end 
if a<=0 
   error('invalid value for a') 
end 
V=sqrt((pi-2)/(2*(a^2))); 
X=5*V; 
while (a^2)*X*exp(-((a*X)^2)/2) > 1e-6 
   X=X+V; 
end 
x=[0:X/samples:X]; 
p=(a^2).*x.*exp(-((a*x).^2)./2); 
pdf=[0 1; x' p']; 
if ispf(pdf)==0 
   p=p./ttlprob(pdf); 
   pdf=[0 1; x' p']; 
end