Conferencistas Internacionais

Over/Under-Dispersed Poisson Distributions and Processes

Prof. N. Balakrishnan (McMaster University-Canada)

In this talk, I will establish several connections of the Poisson weight function to overdispersion and underdispersion. Specifically, I will show that the logconvexity (logconcavity) of the mean weight function is a necessary and sufficient condition for overdispersion (underdispersion) when the Poisson weight function does not depend on the original Poisson parameter. I will also discuss some properties of the weighted Poisson distributions (WPDs). I will then introduce a notion of pointwise duality between two WPDs and discuss some associated properties. Next, after presenting some illustrative examples and providing a discussion on various Poisson weight functions used in practice, I will make some concluding remarks. Finally, I will use these results to introduce and discuss over/under-dispersed Poisson processes.