Date of Award

Spring 2010

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Sunil Kumar Dhar

Second Advisor

Manish Chandra Bhattacharjee

Third Advisor

Sundarraman Subramanian

Fourth Advisor

Wenge Guo

Fifth Advisor

Aridaman Kumar Jain

Sixth Advisor

Ganesh Subramanian


This dissertation studied systems with several components which were subject to different types of failures. Systems with two components having frequency counts in the domain of positive integers, and the survival time of each component following geometric or mixture geometric distribution can be classified into this category. Examples of such systems include twin engines of an airplane and the paired organs in a human body. It was found that such a system, using conditional arguments, can be characterized as multivariate geometric distributions. It was proved that these characterizations of the geometric models can be achieved using conditional probabilities, conditional failure rates, or probability generating functions. These new models were fitted to real-life data using the maximum likelihood estimators, Bayes estimators, and method of moment estimators. The maximum likelihood estimators were obtained by solving score equations. Two methods of moments estimators were compared in each of the several bivariate geometric models using the estimated bias vectors and the estimated variance-covariance matrices. This comparison was done through a Monte-Carlo simulation for increasing sample sizes. The Chi-square goodness-of-fit tests were used to evaluate model performance.

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Mathematics Commons