Code covered by the BSD License

# Generation of Random Variates

### James Huntley (view profile)

generates random variates from over 870 univariate distributions

nbin_cdf(x,r,p)
```function y = nbin_cdf(x,r,p)
%NBIN_CDF Negative binomial cumulative distribution function.
%   Y=NBIN_CDF(X,R,P) returns the negative binomial cumulative distribution
%   function with parameters R and P at the values in X.
%
%   The size of Y is the common size of the input arguments. A scalar input
%   functions as a constant matrix of the same size as the other inputs.
%
%   The algorithm uses the cumulative sums of the binomial masses.

%   B.A. Jones 1-24-95
%   Copyright 1993-2000 The MathWorks, Inc.
%   \$Revision: 2.10 \$  \$Date: 2000/05/26 18:53:03 \$

if nargin < 3,
error('Requires three input arguments.');
end

scalarrp = (prod(size(r)) == 1 & prod(size(p)) == 1);

[errorcode x r p] = distchck(3,x,r,p);

if errorcode > 0
error('Requires non-scalar arguments to match in size.');
end

% Initialize Y to 0.
y=zeros(size(x));

% Compute Y when 0 < X.
xx = floor(x);
k = find(xx >= 0);

% Accumulate the binomial masses up to the maximum value in X.
if any(k)
val = max(max(xx));
if scalarrp
tmp = cumsum(nbin_pdf(0:val,r(1),p(1)));
y(k) = tmp(xx(k) + 1);
else
idx = [0:val]';
compare = idx(:,ones(size(k)));
index = xx(k);
index = index(:);
index = index(:,ones(size(idx)))';
rbig = r(k);
rbig = rbig(:);
rbig = rbig(:,ones(size(idx)))';
pbig = p(k);
pbig = pbig(:);
pbig = pbig(:,ones(size(idx)))';
y0 = nbin_pdf(compare,rbig,pbig);
indicator = find(compare > index);
y0(indicator) = zeros(size(indicator));
y(k) = sum(y0,1);
end
end

% Make sure that round-off errors never make P greater than 1.
k = find(y > 1);
if any(k)
y(k) = ones(size(k));
end

% Return NaN if any arguments are outside of their respective limits.
k1 = find(r < 1 | p < 0 | p > 1 | round(r) ~= r | x < 0);
if any(k1)
tmp = NaN;
y(k1) = tmp(ones(size(k1)));
end
```