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Doubly periodic non-homogeneous Poisson models for hurricane data
Authors:Yi Lu,Jos   Garrido
Affiliation:Department of Mathematics and Statistics, Concordia University, Canada
Abstract:
Non-homogeneous Poisson processes with periodic claim intensity rate have been proposed as claim counts in risk theory. Here a doubly periodic Poisson model with short- and long-term trends is studied. Beta-type intensity functions are presented as illustrations. The likelihood function and the maximum likelihood estimates of the model parameters are derived.Doubly periodic Poisson models are appropriate when the seasonality does not repeat exactly the same short-term pattern every year, but has a peak intensity that varies over a longer period. This reflects periodic environments like those forming hurricanes, in alternating El Niño/La Niña years. An application of the model to the data set of Atlantic hurricanes affecting the United States (1899–2000) is discussed in detail.
Keywords:Non-homogeneous Poisson process   Claim intensity function   Periodicity   Doubly periodic Poisson model   Maximum likelihood estimation   Hurricanes   El Niñ  o/La Niñ  a
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