(R2070) Poisson-Exponentiated Weibull Distribution: Properties, Applications and Extension

In this article, we introduce a new member of the Poisson-X family namely, the Poisson-exponentiated Weibull distribution. The statistical as well as the distributional properties of the new distribution are studied, and the performance of the maximum likelihood method of estimation is verified by a simulation study. The flexibility of the distribution is illustrated by a real data set. We develop and study a reliability test plan for the acceptance or rejection of a lot of products submitted for inspection when their lifetimes follow the new distribution. A real data example is also given to illustrate the feasibility of the sampling plan developed. Later, we introduce a bivariate analogue of the Poisson-exponentiated Weibull distribution called the Farlie-Gumbel-Morgenstern bivariate Poisson-exponentiated Weibull distribution and consider the concomitants of order statistics that arise from this bivariate distribution. The distribution theory of the concomitants of order statistics is also developed