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## Negative binomial distribution functions using R

### 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:

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.