## Mathematics & Statistics Theses & Dissertations

Summer 1997

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mathematics and Statistics

#### Program/Concentration

Computational and Applied Mathematics

Ram C. Dahiya

Dayanand N. Naik

Larry Lee

Edward Markowski

#### Abstract

In this dissertation, we consider a model based approach to the estimation of exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We also consider the analysis of a proportional hazards survival model for randomly censored observations, known as the Koziol-Green model. The model assumes that the lifetime survivor function is a power of the censored time survivor function.

In Chapter 2, we introduce the model based approach to the estimation of the exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We assume that in the beginning of a fishing season M number of fishes are captured, marked and then released back into the population. Also, there are N available sampling units out of which n are sampled by the creel survey agents. The agents observe the number of fish captured with and without tags in each sampled unit. We make two basic assumptions, (1) the number captured in each unit follows a Poisson distribution and (2) the number recaptured given the number captured in each unit follows a binomial distribution. We obtain the maximum likelihood estimator and the moment estimator of the exploitation rate. We also compare the performance of these two estimators. In Chapter 3, the model based approach of Chapter 2 is extended to the case where the space-time units of the fisheries are stratified according to the different fishing areas or seasons.

In Chapter 4, we consider the Koziol-Green survival model with the lifetimes following a Weibull distribution. We consider the Bayesian analysis of this model by specifying parametric prior distributions for the parameters of the model. The method of Gibbs sampler is used for Bayesian computations. The Bayes estimator is compared with the maximum likelihood estimator of the survivor function. In Chapter 5, we incorporate covariates in the Koziol-Green model and study their effect on the lifetimes. We consider maximum likelihood estimation of the parameters of this model.

#### DOI

10.25777/actv-zj53

9780591603941

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