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A parametric model for heterogeneity in paired poisson counts

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  • Goutis, Constantinos
  • Galbraith, Rex F.

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.

Suggested Citation

  • Goutis, Constantinos & Galbraith, Rex F., 1995. "A parametric model for heterogeneity in paired poisson counts," DES - Working Papers. Statistics and Econometrics. WS 10348, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10348
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    Cited by:

    1. Goutis, Constantinos, 1996. "Nonparametric estimation of a mixing density via the kernel method," DES - Working Papers. Statistics and Econometrics. WS 10437, Universidad Carlos III de Madrid. Departamento de Estadística.

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    Keywords

    Wishart distribution;

    Statistics

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