Speaker: Rong Zhu, McMaster University
Title: A New Property of Generalized Poisson and Comparison with Negative
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.