On the Double Prior Selection for the Parameter of Poisson Distribution

by Abdul Haq and Muhammad Aslam.

Abstract: This paper provides a comparison of double informative priors which are assumed for an unknown parameter of Poisson distribution. The idea is that some time for a single true unknown parameter, different prior information are available; usually we use one informative prior to incorporate that prior knowledge and ignoring the other information. So to include two different kind of information in the analysis, two different priors have been selected for a single unknown parameter of Poisson distribution. We have assumed three double priors: Gamma-Chi-square distribution, Gamma-Exponential distribution, Chi-square-Exponential distribution and one as usual prior: Gamma distribution for the unknown parameter of the Poisson model. The comparison is based upon the posterior variances, posterior predictive variances and the posterior predictive probabilities. An application to real life data is also introduced to illustrate the method. Finally a suitable double prior for the unknown parameter of a Poisson distribution is suggested.

Key Words: Density kernel, Informative prior, Posterior distribution, Posterior predictive distribution, Predictive intervals, Predictive probabilities, Prior distribution

Abdul Haq, aaabdulhaq@yahoo.com
Muhammad Aslam, aslamsdqu@yahoo.com

Editor: Bhattacharjee, Dibyojyoti, lecturer_dibyo@yahoo.com

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