Estimating functions of exponential parameters

Malwane M. A Ananda, Purdue University

Abstract

In exponential distribution with location and scale parameters, estimation problems of: (i) reliability function, (ii) density at a given point, (iii) ratio of location and scale parameters and, (iv) restricted location parameter, are considered. For known location parameter, the Bayes nature of the best unbiased estimator of the reliability function and density at a point are established. The admissibility of the best unbiased reliability estimator and the inadmissibility of the unbiased density estimator are proved. In both cases the admissibility of a class of related generalized Bayes estimators is established. For unknown location and scale parameters, the best unbiased reliability estimator has a generalized Bayes structure. The nonexistence of the unbiased density estimator is noticed and, as its substitute, the corresponding Bayes rule is derived. In both cases, admissibility of a class of related generalized Bayes estimators within the class of all scale equivariant procedures is established. Along with some practical recommendations, numerical and asymptotical studies of quadratic risk functions are presented. Admissible estimators of one-parameter exponential reliability function in the case of a type II censored sample is given for a system in a series. For the estimation of restricted location parameter and the ratio of location and scale parameters, estimators which improve upon traditional estimators, are found and related generalized Bayes procedures are discussed.

Degree

Ph.D.

Advisors

Rukhin, Purdue University.

Subject Area

Statistics

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