mnbinrnd

A generator MNBINRND and a density function MNBINPDF

In many experimental settings in the life sciences, aggregated count data needs to be analyzed, for example, the number of mites on leaves of a tree, or the number of parasites found in hosts. This data is often well-described by a negative-binomial distribution.


Although Matlab's statistical toolbox has negative-binomial functions, they are parametrized for a limited form of the distribution based on the expected number of Bernoulli events needed to achieve a number of successes. The parameters are the event probability, P, and a positive integer aggregation constant, R, the number of successes.


The more general form is parametrized with a mean count W and an aggregation K. W and K are related to the traditional parameters P and R by the expressions:

P = K/(K + W) and K = R,


with the distinction that K is any positive real number, not just positive integers.

Here I provide two functions for the more general form, a generator MNBINRND and a density function MNBINPDF.
Requires the Statistics Toolbox.