Speaker: Rong Zhu, McMaster University

Title: A New Property of Generalized Poisson and Comparison with Negative

Binomial

SUMMARY

We prove that the generalized Poisson distribution

GP(theta, eta) (eta >=0) is a mixture of Poisson distributions;

previously it was only known to be overdispersed relative to Poisson

like negative binomial distribution. We compare the probability mass

functions and skewnesses of the generalized Poisson and the widely

used negative binomial distributions with the first two moments fixed.

We find that the generalized Poisson and negative binomial distributions

with means and variances fixed have slight differences in many situations,

but their zero-inflated distributions with masses at zero, means and

variances fixed can differentiate largely. These probabilistic comparisons

are helpful in selecting a better fitting distribution for modelling count

data with heavy right tails. Through a real example of count data with

large zero fraction, we illustrate how the generalized Poisson and

negative binomial distributions as well as their zero-inflated

distributions can be discriminated.

This is a joint work with Dr. Harry Joe.