Bayes estimators of parameters of Poisson type exponential class software model considering generalized Poisson and gamma priors

Article type: Research Article

Authors: Singh, Rajesh^{a; *} | Vidhale, A.A.^a | Carpenter, Mark^b

Affiliations: [a] Department of Statistics, S. G. B. Amravati University, Amravati – 444 602, India | [b] Department of Mathematics and Statistics, Auburn University, Auburn, USA

Correspondence: [*] Corresponding author. E-mail: rsinghamt@hotmail.com.

Abstract: The paper deals with the estimation problem of Poisson type Exponential Class model which has wide application in software reliability. This model consists of two parameters namely, the total number of failures and the failure rate. Considering the behaviour of the parameter, total number of failure and limitation of Poisson distribution, a generalized Poisson distribution has been proposed as a prior for this parameter. Further, an inverted Gamma prior has been selected for failure rate in view of its property. The Bayes estimators have been obtained considering these priors under Squared Error Loss Function. To study the performance of obtained estimators, these estimators have been compared with corresponding maximum likelihood estimators on the basis of a Monte Carlo simulation study.

Keywords: Bayes estimators, gamma distribution, generalized Poisson distribution, prior & posterior distributions and relative efficiency

DOI: 10.3233/MAS-2009-0109

Journal: Model Assisted Statistics and Applications, vol. 4, no. 2, pp. 83-89, 2009