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Document Details :

Title: A Damaged Generalised Poisson Model and Its Application to Reported and Unreported Accident Counts
Author(s): SCOLLNIK, David P.M.
Journal: ASTIN Bulletin
Volume: 36    Issue: 2   Date: 2006   
Pages: 463-487
DOI: 10.2143/AST.36.2.2017930

Abstract :
This paper investigates some models in which non-negative observations from
a Poisson or generalised Poisson distribution are possibly damaged according
to a binomial or quasi-binomial law. The latter case is appropriate when the
observations are over-dispersed. Although the extent of the damage is not
known, it is assumed that the event of whether or not damage occurred is discernible.
The models are particularly suited for certain applications involving
accident counts when evidence of certain accidents may be observed even though
the accidents themselves may go unreported. Given the number of observed
accidents and knowledge as to whether or not some additional accidents have
gone unreported, these models may be used to make inferences concerning the
actual number of unreported and total number of accidents in the current period,
and the numbers of reported, unreported, and/or total accidents in a future
period. The models are applied to a real data set giving reported and unreported
patient accidents in a large hospital. Both maximum likelihood and Bayesian
estimation methods are presented and discussed.