Poisson modified weibull distribution with inferences on stress-strength reliability model

This paper is devoted to study a new four-parameter model called a Poisson Modified Weibull Distribution (PMW). The motivation for the new distribution is to obtain the hazard rate function with multiple shapes, the most important of which is the bathtub shape which is very useful in the reliability analysis. Some of its statistical properties are discussed. Maximum likelihood, method of moments and Bayesian techniques are used for estimating the parameters and the Fisher's information matrix is presented. In specific, we focus on the study of Stress- Strength reliability parameter, R=P(Y<X)$R\ = P(Y < X)$, when X$X$ andY$\ Y$ have a PMW distribution. The maximum likelihood and Bayesian estimators for R$R$ are derived. A simulation study is performed to compare the performance of each method of estimation. Moreover, the goodness of fit for PMW distribution comparison with other models are carried out by means of two applications to real data sets to illustrate the flexibility of the proposed model. Finally, the Stress-Strength model for PMW distribution was applied to a real data representing the failure times for two types of electrical insulators.