A new family of Poisson-exponential distributions with applications to cancer data and glass fiber reliability

Towards the end of the 20th century, statisticians were keen to create new distribution families that would meet the rapid advancements in modeling and application domains while also getting around constraints on certain distributions. In this study, a new family is proposed for adding one parameter to a continuous distribution by using countable mixture of PE distribution. Some attributes such as the probability density function extreme stability, and the hazard rate function of the new family are provided. As a member of the purpose family, a Weibull distribution illustration is presented. Poisson exponential Weibull (PE-W) characteristics such as compound, moments, skewness, kurtosis, and others are derived. Using both complete and censored data sets as well as simulated experiments, the maximum likelihood estimation of PE-W parameters was examined. Further, to illustrate the value of the PE-W distribution compared to other commonly used distributions, an analysis is carried out on actual and censored data sets that represent the breaking stress of carbon fibers and liver (lung) cancer.