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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

nbinordk_pdf(n, k, p, r, b)
% nbinordk_pdf.m - evaluates a Negative Binomial Order K Probability denisity.
%   See "Univariate Discrete Distributions", Johnson, Kemp, and Kotz,
%   Wiley, p.458, 2005.  See also "http://mathworld.wolfram.com/Partition.html".
%
%   For nn = 40 (& p=0.5), 'distribs20.m' requires ~45 minutes to generate 1000 points!!!
%
%   Created by  J. Huntley,  7/19/07.
%
%   Loads files 'partition1-N.dat'
%

function [pdf] = nbinordk_pdf(n, k, p, r, b)

%persistent q logqdp

%Initializations.
%if(isempty(q))
    q = 1 - p;
    logqdp = log(q/p);
%end

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

    % 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) = factorial(x(jc));
            fx(jc) = gammaln(x(jc)+1);
        end
        sumx = sum(x);
        %pfx = prod(fx)*(b-1);
        pfx = sum(fx) + gammaln(b);
        %sum1 = sum1 + factorial(sumx+b-1)*(q/p)^sumx / pfx;
        sum1 = sum1 + exp(gammaln(sumx+b)+ sumx*logqdp - pfx);
    end
    pdf = coef * sum1;
end  % (n-k) > 0

return


    

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