Publication Date

1988

Document Type

Dissertation/Thesis

First Advisor

Lingham, Rama

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences

LCSH

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

Abstract

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.

Comments

Bibliography: pages [131]-133.

Extent

viii, 169 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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