On weighted distribution with applications to goodness-of-fit testing

Abstract This paper develops a reformulation of the weighted distribution model based on a transformation of the weight function. This reformulated model encompasses several well-known families, including the gamma, Weibull, beta, beta prime, generalized gamma, half-normal, logistic, and chi-square distributions. The primary objective of this work is to apply the reformulated version to develop a new characterization-based goodness-of-fit test for lifetime distributions. Moreover, the flexibility of the reformulated version of the weighted distribution facilitates the construction of new flexible probability distributions. We demonstrate this fact through real data modeling, where a weighted model exhibits greater flexibility than the corresponding baseline model. We further investigate several reliability properties of the proposed model.