Negative binomial mass probability function R's dnbinom function returns the probability of observing a count (f), as predicted by the negative binomial model, given a 'shape' (or 'size') parameter (k) and mean (m). For example: f=5 # enter count k=2 # enter shape parameter m=3 # enter mean # probability of f given F dnbinom(f, s=k, mu=m) Gave: [1] 0.0746496 Note: Although shape parameters equal to zero and infinity are theoretically possible, these functions will not accept those limiting values. When k is above around 10^10, use a Poisson function (with the same mean). To obtain the expected proportion for each of a range of outcomes, you need to use an ordered list of counts instead of a single value, for example as dnbinom(0:10, s=k, mu=m) If you wish to fit the negative binomial distribution to a set of observed frequencies, and variable y contains those frequencies, given an estimate of k, you could find their expected number of each count using dnbinom(0:max(y), s=k, mu=mean(y))*tot(y) Negative binomial cumulative distribution function R's pnbinom function returns the probability of observing a count less than or equal to a given count. Negative binomial inverse distribution function R's qnbinom function does the opposite of its pnbinom function - that is it returns the relevent quantile (again a count). Negative binomial random function R's rnbinom function gives 1 (or more) counts randomly selected from the specified negative binomial distribution(s). For example, rnbinom(5, s=3, m=2) would provide 5 counts randomly selected from a negative binomial distribution whose mean is 2, and shape parameter (k) is 3.