On Bayesian Estimation of the Product of Poisson Rates with Application to Reliability

ABSTRACT

This article derives a non informative prior for a product of k independent Poisson rates, i.e., , thereby considering the problem of estimating the product. Based on the prior, a procedure for obtaining posterior quantiles and HPD interval of the product is suggested. The procedure provides a facile solution for both distributional specification and computational implementation, whose outputs are readily adapted for required inference summaries. A salient feature of the procedure is that it provides a unified method for estimating various types of the product, thereby solving all the existing problems (involved in estimating the product) simultaneously and satisfactorily, at least within the Bayesian framework. In the three examples provided, practical applications of the procedure to reliability are well described.

Keywords:

• HPD interval
• Non informative prior
• Product of Poisson rates
• Reliability
• Weighted Monte Carlo method

Mathematics Subject Classification:

• Primary 62F15
• Secondary 62N05

Acknowledgment

The author would like to thank the referees and the associate editor for their careful reading of the manuscript and for suggestions, which improved the presentation of this article.