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.
George, Alphonsa and George, Dais
(R2070) Poisson-Exponentiated Weibull Distribution: Properties, Applications and Extension,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 18,
2, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol18/iss2/3