Inference for Kumaraswamy‐G family of distributions under unified progressive hybrid censoring with partially observed competing risks data

Abstract

In this study, statistical inference for competing risks model with latent failure times following the Kumaraswamy‐G (Kw‐G) family of distributions under a unified progressive hybrid censoring (UPHC) scheme is developed. Maximum likelihood estimates (MLEs) of the unknown model parameters are obtained, and their existence and uniqueness properties are discussed. Using the asymptotic properties of MLEs, the approximate confidence intervals for the model parameters are constructed. Further, Bayes estimates with associated highest posterior density credible intervals for the model parameters are developed under squared error loss function with informative and noninformative priors. These estimates are obtained under both restricted and nonrestricted parameter spaces. Moreover, frequentist and Bayesian approaches are developed to test the equality of shape parameters of the two competing failure causes. The comparison of censoring schemes based on different criteria is also discussed. Monte Carlo simulation studies are used to evaluate the performance of the proposed statistical inference procedures. An electrical appliances data set is analyzed to illustrate the applicability of the proposed methodologies.