A parametric model for heterogeneity in paired poisson counts

Constantinos Goutis and Rex F. Galbraith

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: \Ve present a model for data in the form of match pairs of counts. Our work is motivated by a problem in fission track analysis, where the determination of a crystal age is based on the ratio of counts of spontaneous and induced tracks. It is often reasonable to assume that the counts follow a Poisson distribution but, typically, they are overdispersed and there exists a positive correlation between the numbers of spontaneous and induced tracks at the same crystal. We propose a model that allows for both overdispersion and correlation by assuming that the mean densities follow a bivariate Wishart distribution. Our model is quite general, having the usual negative binomial or Poisson models as special cases. \Ve propose a maximum likelihood estimation method based on a stochastic implementation of the EM algorithm and we derive the asymptotic standard errors of the parameter estimates. vVe illustrate the method by a data set of fission tracks counts in matched areas of zircon crystals.

Keywords: Wishart; distribution; EM; algorithm; Fission; track; analysis; Maximum; likelihood; estimation; Overdispersion (search for similar items in EconPapers)
Date: 1995-12
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:10348

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