Goodness of fit test for lifetime distributions usung Stein's type characterizations

Abstract

This thesis focuses on the development of new goodness-of-fit tests for lifetime distributions, an area of importance in both reliability theory and survival analysis. Lifetime data often arise in engineering and biomedical studies, where assumptions regarding the underlying probability distribution form the basis for subsequent inference. Therefore, it is essential to validate these assumptions through appropriate goodness-of-fit procedures. The central methodology of this work is based on Stein’s type identity, which has proven to be a powerful tool in distributional characterizations. While Stein’s identity is classical for the normal distribution, recent research has extended such characterizations to a broader class of probability distributions. Motivated by these developments, we construct goodness-of-fit tests for four important lifetime distributions: gamma, Rayleigh, inverse Gaussian, and Lindley. For each distribution, we employ characterization results based on Stein’s type identity to define suitable departure measures and develop test statistics within the framework of U-statistic theory. A key contribution of this study lies in addressing the problem of censoring, which is a common feature of lifetime data but not adequately handled in much of the existing literature. We extend the proposed test procedures to right-censored data, analyze their asymptotic properties using central limit theorems for U-statistics, and establish their validity under both censored and uncensored scenarios. The performance of the proposed tests is investigated through extensive Monte Carlo simulation studies, where their power is compared with existing procedures. The results demonstrate that the developed tests provide reliable performance in finite samples. To illustrate practical utility, the methods are applied to real-life data sets from reliability and biomedical contexts.