Contributions to Parametric and Nonparametric Inference in Life Testing

Abstract

<p>In this thesis, we consider both nonparametric and parametric inference in life-testing. Under nonparametric inference, we study the nonparametric precedence test and some alternatives. We first introduce a general maximal precedence test for testing the hypothesis that two distribution functions are equal, which is a variation of the precedence life-test discussed earlier in the literature. Next, we introduce three Wilcoxon-type rank-sum precedence tests, which in fact generalize the classical Wilcoxon rank-sum test for Type-II censored data. We propose the use of Edgeworth expansion to approximate the null distributions of these test statistics. Finally, we introduce another generalization of the precedence and maximal precedence tests, viz., weighted precedence and maximal precedence tests, by giving weights to the precedence failures. We also extend these tests to the case of progressive Type-II censoring. We examine the power properties of these test statistics and compare them with those of the precedence and maximal precedence tests under Lehmann alternative as well as the location-shift alternative. Under parametric inference, we first propose the use of EM-algorithm to determine maximum likelihood estimators (MLE's) when the data are progressively Type-II censored. We explain how one could obtain the variances and covariances as well as the standard errors of the MLEs by using the missing information principle. Next, we discuss point and interval estimation for the normal distribution under progressive censoring. Then, we concentrate on the Wei bull lifetime model under progressive censoring and discuss the determination of optimal censoring schemes. Finally, construction of progressively-sensored reliability sampling plans is discussed. Next, we discuss goodness-of-fit tests based on spacings under progressive censoring. We propose a test for exponentiality based on spacings from a progressively Type-II censored sample. We then generalize this test to a general location-scale family of distributions. We use a simulation study to investigate the power of this test under several different alternatives. Finally, we study the estimation of the parameters of a two-parameter BirnbaumSaunders distribution based on complete and Type-II censored samples. For the complete sample situation, we study the MLE's and propose and study modified moment estimators, simple bias-corrected estimators, and jackknifed estimators, and all their asymptotic distributions. For the Type-II censored sample situation, we discuss the MLE and derive the asymptotic variance-covariance matrix of the MLE's. A Monte Carlo EM-algorithm for the determination of the MLE's is discussed. We also propose a simple bias correction technique. Asymptotic confidence intervals based on these estimators and their probability coverages are examined.</p>