Page "Negative binomial distribution" Paragraph 1

The Pascal distribution ( after Blaise Pascal ) and Polya distribution ( for George Pólya ) are special cases of the negative binomial.

There is a convention among engineers, climatologists, and others to reserve “ negative binomial ” in a strict sense or “ Pascal ” for the case of an integer-valued stopping-time parameter r, and use “ Polya ” for the real-valued case.

The Polya distribution more accurately models occurrences of “ contagious ” discrete events, like tornado outbreaks, than the Poisson distribution by allowing the mean and variance to be different, unlike the Poisson.

“ Contagious ” events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term.