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Generation of Random Variates

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Generation of Random Variates

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generates random variates from over 870 univariate distributions

skewgent_pdf(x, mu, sigma, n, k, lambda)
% skewgent_pdf.m - evaluates a Skewed Generalized T Probability Density.
%   See "Cyclicality in Catastrophic and Operational Risk Measurements", 
%   L Allen and T.G. Bali, CUNY.
%
%   Vector Form of PDF !!!
%
%  Created by Jim Huntley,  8/24/06
%

function [pdf] = skewgent_pdf(x, mu, sigma, n, k, lambda)

A = beta(2/k,(n-1)/k)/sqrt(beta(1/k,n/k))/sqrt(beta(3/k,(n-2)/k));
S = sqrt(1+3*lambda^2-4*A^2*lambda^2);
theta = (k/(n-2))^(1/k)*sqrt(beta(1/k,n/k))/sqrt(beta(3/k,(n-2)/k))/S;
C = k / ((2*(n-2)/k)^(1/k)*theta*beta(1/k,n/k));
delta = 2*lambda*A/S;

sx = size(x,2);

for jx = 1:sx
    epsi = x(jx) - mu + delta*sigma;
    pdf(jx) = C * (1 + (abs(epsi))^k/((n-2)/k)/(1+sign(epsi)*lambda)^k/theta^k/sigma^k)^((-n+1)/k) / sigma;    
end 

return

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