Author

Jie Huang

Date of Award

8-2013

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Ramesh Gupta

Second Committee Member

Pushpa Gupta

Third Committee Member

Andrew Knightly

Abstract

In life testing and survival analysis, sometimes the components are arranged in series or parallel system and the number of components, say Z, is initially unknown. Thus, the number of components is considered as random with an appropriate probability mass function. More specifically, the problem arises in cancer clinical trials where the number (Z) of metastasis-competent cells (clonogens) is unknown and the event occurs as soon as one of the clonogens metastasizes. In damage models, the number of cracks is unknown and the system fails as soon as the first failure occurs. In this connection, several distributions of Z have been considered in the literature, including the Poisson distribution, the logarithmic series distribution, the COM-Poisson distribution and the power series distribution, with exponential as the baseline distribution. More recently, Gupta et al. [1] proposed a model with the generalized Poisson distribution as the distribution of Z.

With exponential as the baseline distribution, the resulting model has decreasing failure rate. In this thesis, we will model the survival data with baseline distribution as Weibull and the distribution of Z as generalized Poisson, giving rise to four parameters in the model and increasing, decreasing, bathtub and upside bathtub failure rate. The maximum likelihood estimation of the parameters will be studied and the results will be compared to the existing models, especially the exponential generalized Poisson distribution which has been studied by Gupta et al. [1].

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