University of Edinburgh
School of Mathematics
Statistics seminar
Date: Monday 12 April 2010 at 2pm
Location: 5215 JCMB
N. Balakrishnan (McMaster University)
Over/Under-Dispersed Poisson Distributions and Processes
Abstract.
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.
Tea and coffee will be available after the seminar in the Mathematics
Common Room (5212).
**Note the new webpage for the seminar:**
http://www.maths.ed.ac.uk/~nbochkin/StatisticsSeminar.html
Natalia
PS JCMB stands for James Clerk Maxwell Building, at King's
Buildings campus:
www.ed.ac.uk/maps/
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