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Non–homogenous 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.
Double periodic Poisson models are appropriate when the seasonality does not repeat the exact 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 Nino/La Nina years. An application of the model to the dataset of Atlantic Hurricanes Aﬀecting the United States (1899-2000) is discussed in detail.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Lu, Yi and Garrido, Jose|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 4/04|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Non–homogeneous Poisson process, Claim intensity function, Periodicity, Double periodic Poisson model, Maximum likelihood estimation, Hurricanes, El Nino/La Nina.|
|Deposited By:||ANDREA MURRAY|
|Deposited On:||03 Jun 2010 15:32|
|Last Modified:||08 Dec 2010 18:26|
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