A Nonhomogeneous Poisson Hidden Markov Model for Claim Counts

Abstract We propose a nonhomogeneous Poisson hidden Markov model for a time series ofclaim counts that accounts for both seasonal variations and random fluctuations in the claims intensity. It assumes that the parameters of the intensity function for the nonhomogeneous Poisson distribution vary according to an (unobserved) underlying Markov chain. This can apply to natural phenomena that evolve in a seasonal environment. For example, hurricanes that are subject to random fluctuations (El Niño-La Niña cycles) affect insurance claims. The Expectation-Maximization (EM) algorithm is used to calculate the maximum likelihood estimators for the parameters of this dynamic Poisson hidden Markov model. Statistical applications of this model to Atlantic hurricanes and tropical storms data are discussed.

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