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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

ippois_pdf(n, lambda, rho)
% ippois_pdf.m - evaluates an Inflated Parameter Poisson Probability denisity.
%   See "Inflated-Parameter Family of Generalized Power Series Distributions
%   and their Application in Analysis of Overdispersed Insurance Data", 
%   N. Kolev et al. ARCH 00V211.PDF
%
%  Created by Jim Huntley,  10/27/09
%
%   Loads files 'partition1-N.dat'
%

function [pdf] = ippois_pdf(n, lambda, rho)

%persistent loglam1mr logrho pn

%Initializations.
%if(isempty(pn))
    pn = exp(-lambda);
    loglam1mr = log(lambda*(1-rho));
    logrho = log(rho);
%end

% Evaluate PDF.
if(n == 0)
    pdf = pn;

elseif(n > 0)
    % Fetch pre-stored partitions of 'n'. Frequencies returned in array, "d".
    pname = ['partition' num2str(n)];
    load(pname, 'd');            
    spc = size(d,2);
    d = double(d);

    % Calculate PDF.
    % Sum over all partition frequencies to get solution to Diophantine Equation. 
    sum1 = 0;
    d1 = size(d,1);
    for jr = 1:d1
         for jc = 1:spc
            x(jc) = d(jr,jc);
            dx(jc) = (jc-1) * x(jc);
            %fx(jc) = factorial(x(jc));
            fx(jc) = gammaln(x(jc)+1);
        end
        sumx = sum(x);
        sumdx = sum(dx); 
        %pfx = prod(fx);
        pfx = sum(fx);
        %sum1 = sum1 + (lambda*(1-rho))^sumx * rho^sumdx / pfx;
        sum1 = sum1 + exp(sumx*loglam1mr + sumdx*logrho - pfx);
    end
    pdf = pn * sum1; 

end % conditional for n > 0.

return


    

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