Date of Award

4-1996

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Supervisor

N. Balakrishnan

Abstract

This thesis is presented in three sections: Section One (Progressive Type-II Censoring). Section Two (Generalized Distributions) and Section Three (Conclusions). In Section One of the thesis, a method of censoring known as progressive Type-II censoring is presented. Mathematical properties of the progressive Type-II censored order statistics arising from this type of censoring are established for particular as well as arbitrary distributions. Applications to inference, including best linear unbiased estimation and maximum likelihood estimation, are discussed, as well as simulation, and the question of optimal censoring patterns is also addressed through an extensive computational study. Section Two of the thesis concerns generalized distributions. Here, we introduce a shape parameter to the logistic and half logistic distributions and discuss the properties of the resulting distributions. Many recurrence relations for single and product moments of order statistics from these distributions are established. Best linear unbiased, maximum likelihood and moment estimation of parameters arising from these distributions are considered, and truncated versions of the distributions are also examined. Finally, we conclude with a number of questions and open problems which have yet to be addressed in the future.

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Mathematics Commons

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