Publication Date


Document Type


First Advisor

Lingham, Rama

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences


Estimation theory; Monte Carlo method; Distribution (Probability theory)


The theory of first passage times finds many applications in applied probability, engineering, and the physical and natural sciences. Oftentimes, it is computationally tedious, if not impossible, to determine parameters of first passage time distributions. This thesis investigates crude and conditional Monte Carlo estimators of some properties of first passage time distributions of discrete state space Markov processes. The conditional Monte Carlo estimators are based on observed hazard rates, which are defined as conditional probabilities of failure at time t given survival up to that time and a complete history of the process. This thesis includes numerical examples of the estimation procedures and comparisons of the crude and Monte Carlo estimators. Specifically, the relative efficiency over the crude estimator of each conditional estimator is computed. Plots of the empirical distribution function of each estimator are also given. Results show that, under certain conditions, the conditional Monte Carlo estimators are more efficient than the crude Monte Carlo estimator.


Bibliography: pages [131]-133.


viii, 169 pages




Northern Illinois University

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