## Electronic Theses and Dissertations

#### Title

Inference procedures in some lifetime models.

1992

Dissertation

Ph.D.

#### Department

Mathematics and Statistics

Statistics.

CC BY-NC-ND 4.0

#### Abstract

This thesis deals with inference procedures for some parametric lifetime models, involving single as well as multiple samples. In some situations censored (Type I and Type II) samples are considered. The thesis consists of two parts. Part I deals with homogeneity testing involving multiple samples from the gamma, exponential and the Weibull or the extreme value distributions. Part II deals with confidence interval procedures for the parameters of the two parameter exponential distribution and the extreme value models. Assuming the underlying distribution for several groups of data to be two parameter gamma with common shape parameter various tests are developed for comparing the means of the groups. The performance of these test statistics are determined in terms of level and power by conducting simulations. A C($\alpha$) test and a likelihood ratio test are presented and compared for checking the validity of the assumption of common shape parameter. Under failure censoring, various test statistics for comparing the mean life times of several two parameter exponential distributions are derived and studied by performing Monte Carlo simulations. Considering failure censored data, homogeneity tests for extreme value location parameters with the assumption of a common scale parameter are studied. For this problem, a C($\alpha$) test is derived an compared with other existing methods through simulations. Also, for testing the assumption of common extreme value scale parameter, a C($\alpha$) statistic is derived and compared with other existing statistics. In single sample situations several confidence interval estimation procedures for the scale parameter of a two parameter exponential distribution under time censoring are discussed. Behaviours of the confidence intervals based on these procedures are examined by simulation study in terms of average lengths, coverage and tail probabilities. For extreme value failure censored data (with or without covariates), a simple method using orthogonality approach (Cox and Reid, 1987) to obtain explicit expression for the variance-covariance of the MLEs of the parameters is given. For obtaining confidence intervals for the parameters of interest various procedures, such as the procedure based on the likelihood ratio, the procedure based on the likelihood score corrected for bias and skewness and the procedure based on the likelihood ratio adjusted for mean and variance, are derived. The behaviours of these procedures are investigated in terms of average lengths, coverage and tail probabilities by conducting Monte Carlo simulations. The above procedures are extended to extreme value regression model. Confidence interval procedures are also derived and studied for the parameters of the extreme value model under time censoring. Source: Dissertation Abstracts International, Volume: 54-05, Section: B, page: 2583. Thesis (Ph.D.)--University of Windsor (Canada), 1992.

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