Characterization of the weighted power function distribution by reliability functions and moments

Abstract

The characterization is an elegant property of distributions that uniquely defines the associated stochastic model. The power function distribution is a flexible model which is often used for the analysis of income data, lifetime data, and modeling of failure procedures. Weighted distributions have wide applications in real-life problems, where the probabilities of events are observed and recorded by making modifications to probabilities of actual occurrence of events considering methods of ascertainment. In this paper, we considered the weighted power function (WPF) distribution and used some reliability measures to characterize it. We characterized the WPF distribution by various techniques like mean inactivity times, mean residual function, conditional moments, conditional variance, doubly truncated mean, incomplete moments and reverse hazard function.