How can I efficiently calculate the negative binomial cumulative distribution function?

Question

This post is really helpful:

How can I efficiently calculate the binomial cumulative distribution function?

(Title = How can I efficiently calculate the binomial cumulative distribution function?)

However, I need the negative binomial cumulative distribution function.

Is there a way to tweek the code to get a negative cumulative distribution function?

http://www.wolframalpha.com/input/?i=CDF[NegativeBinomialDistribution[10%2C+3%2F4]%2C+4] is VERY efficient :) — Dr. belisarius, Oct 28 '10 at 01:08
You may find the code here http://live.boost.org/doc/libs/1_37_0/boost/math/distributions/negative_binomial.hpp — Dr. belisarius, Oct 28 '10 at 02:24

John D. Cook · Accepted Answer · 2010-10-28T19:38:55.117

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You can compute the CDF by summing the terms of the PMF taking advantage of the recurrence relationship the terms satisfy. The terms in the series are a little complicated, but the ratio of consecutive terms is simple.

edited Oct 28 '10 at 19:38

answered Oct 27 '10 at 23:20

John D. Cook

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Sorry, my mistake. I wrote "PDF" when I meant to say "CDF" -- cumulative density function. "PMF" is probability mass function, the probability of each value. – John D. Cook Oct 28 '10 at 19:40

How can I efficiently calculate the negative binomial cumulative distribution function?

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