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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

compoisok_pdf(n, k, alpha, c)
% compoisok_pdf.m - evaluates a Compound Poisson Order K Probability denisity.
%   See "Univariate Discrete Distributions", Johnson, Kemp, and Kotz,
%   Wiley, p.460, 2005.  See also "http://mathworld.wolfram.com/Partition.html".
%
%   Created by  J. Huntley,  12/07/06.
%
%   Loads 'partition1-N.dat'
%

function [pdf] = compoisok_pdf(n, k, alpha, c)

%persistent odkpa lodkpa coef facm1 

%if(isempty(odkpa))
    %Initializations.
    odkpa = 1 / (k+alpha);
    lodkpa = log(odkpa);
    coef = (alpha *odkpa)^c;
    facm1 = gammaln(c);
%end

if(n == 0)
    pdf = coef;
elseif(n > 0)
    
    % Fetch pre-stored partitions of 'n'. Frequencies returned in array, "d".
    pname = ['partition' num2str(n)];
    load(pname, 'd');            
    d = double(d)
    spc = size(d,2);
    spr = size(d,1);

    % Select rows of 'd' with only min(k,spc) columns populated and store in array, 'xs'.
    indx = 0;
    for jr = 1:spr
        if(size(find(d(jr,k+1:spc)),2)== 0)
            indx = indx + 1;
            dd(indx,:) = d(jr,:);
        end        
    end
    xlim = min(k,spc);
    xs = dd(1:indx,1:xlim);

    % Calculate PDF.
    % Sum over solutions up to order 'k' for Diophantine Equation. 
    sum1 = 0;
    sx1 = size(xs,1);
    for jr = 1:sx1
        for jc = 1:xlim
            x(jc) = xs(jr,jc);
            fx(jc) = gammaln(x(jc)+1);
        end
        sumx = sum(x);
        pfx = sum(fx) + facm1;
        sum1 = sum1 + exp(gammaln(sumx+c) + sumx*lodkpa - pfx);
    end
    pdf = coef * sum1;
end  % n > 0

return


    

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