Date of Award

Summer 8-19-2016

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Ramesh C. Gupta

Second Committee Member

Pushpa L. Gupta

Third Committee Member

Randy (Chu Shing) Lai

Abstract

In survival analysis and reliability studies, problems with random sample size arise quite frequently. More specifically, in cancer studies, the number of clonogens is unknown and the time to relapse of the cancer is defined by the minimum of the incubation times of the various clonogenic cells. In this thesis, we have proposed a new model where the distribution of the incubation time is taken as Weibull and the distribution of the random sample size is Bessel, hence, giving rise to Weibull-Bessel (WB) distribution. The maximum likelihood estimation of the model parameters is studied and a score test is developed to compare it with its special sub-model namely, Exponential-Bessel (EB) distribution. Two real data sets are examined and it is shown that the proposed model, presented here, fits better than several other existing models in the literature. Extensive simulation studies are also carried out to examine the performance of the estimates.

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