Doctoral Dissertations

Abstract

"We develop a saddlepoint-based method and several generalized Bartholomew methods for generating confidence intervals about the rate parameter of an exponential distribution in the presence of heavy random right-censoring. Butler's conditional moment generating function formula is used to derive the relevant moment generating function for the rate parameter score function which provides access to a saddlepoint-based bootstrap method. Moment generating functions also play a key role in the generalized Bartholomew methods we develop. Since heavy censoring is assumed, the possible non-existence of the rate parameter maximum likelihood estimate (MLE) is nonignorable. The overwhelming majority of existing methods condition upon the event that the number of observed failures is non-zero (rate parameter MLE exists). With heavy censoring, these methods may not be able to produce confidence interval an appreciable percentage of times. Our proposed methods are unconditional in the sense that they can produce confidence intervals even when the rate parameter MLE does not exist. The unconditional saddlepoint method in particular defaults in a natural way to a proposed generalized Bartholomew method when the rate parameter MLE fails to exist. We find that the proposed saddlepoint method outperforms competing Bartholomew methods in the presence of heavy censoring and small sample sizes"--Abstract, page iv.

Advisor(s)

Paige, Robert

Committee Member(s)

Samaranayake, V. A.
Wen, Xuerong
Olbricht, Gayla
Du, Xiaoping

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Fall 2012

Pagination

ix, 80 pages

Note about bibliography

Includes bibliographical references (pages 70-73).

Rights

© 2012 Noroharivelo Volaniaina Randrianampy, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Confidence intervals -- Mathematical modelsCensored observations (Statistics)Method of steepest descent (Numerical analysis)

Thesis Number

T 10147

Print OCLC #

843774704

Electronic OCLC #

909370945

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Included in

Mathematics Commons

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