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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

boxcoxt_pdf(x, mu, sigma, nu, tau)
% boxcoxt_pdf.m - evaluates a Box Cox T Probability Density.
%   See BCT, "The GAMLSS Package", 
%   http://cran.r-project.org/doc/packages/gamlss.pdf, p.12.
%
%   Vector Form of PDF !!!
%
%  Created by Jim Huntley,  11/8/07
%

function [pdf] = boxcoxt_pdf(x, mu, sigma, nu, tau)

%persistent coef anu

%if(isempty(coef))
    %coef = gamma(0.5*(tau+1)) / (mu^nu * sigma * gamma(0.5) * gamma(0.5*tau) * sqrt(tau));
    coef = gammaln(0.5*(tau+1)) - (nu*log(mu) + log(sigma) + gammaln(0.5) + ...
           0.5*log(tau) + gammaln(0.5*tau));
    anu = abs(nu);
%end

if(nu == 0)
    z = log(x./mu) ./ sigma;
else
    z = ((x./mu).^nu - 1) ./ (nu * sigma);
end

pdf = exp(coef + (nu-1).*log(x) - 0.5.*(tau+1) .* log(1 + (z.^2)./tau));
% Normalization.
pdf = pdf ./ t_cdf(1/(sigma*anu),tau);

return

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