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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?

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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.

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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.

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