Doctoral Dissertations
Abstract
"The problem of obtaining percentile points and prediction bounds for a future observation, or for an order statistic from a future sample has been of interest to researchers in the area of life-testing. In this research, three life-testing situations are considered, namely (1) obtaining prediction intervals for a future observation or the smallest order statistic from a future sample from a Weibull distribution, (2) obtaining a predictive density for a smallest order statistic from a future sample from a Weibull distribution using data from an accelerated life test and (3) obtaining a predictive density for a future observation from a lognormal distribution using data from an accelerated life test.
The solution for all the problems are based on the Maximum Likelihood Predictive Density method proposed by Lejeune and Faulkenberry in their 1982 JASA paper. This is one of the "predictive likelihood" procedures introduced during the last 20 years and is known as the "profile likelihood" method.
In problem ( 1) a simple method that works under both Type I and Type II censoring is developed. This method provides both lower and upper prediction bounds. In problem (2) we consider Type II censoring and obtain a predictive density that is well known and has closed form expression for percentile points. For problem (3) a t-distribution is obtained as the predictive density.
Monte Carlo simulation is used to investigate the properties of the proposed solutions and modifications. Results show that the methods, though simple, are reasonably accurate"-- Abstract, p. iv
Advisor(s)
Samaranayake, V. A.
Committee Member(s)
Bryant, Richard Ralph
Gan, Gaoxiong
Patel, J. (Jagdish)
Watnik, Mitchell
Department(s)
Mathematics and Statistics
Degree Name
Ph. D. in Mathematics
Publisher
University of Missouri--Rolla
Publication Date
Fall 1998
Pagination
viii, 82 pages
Note about bibliography
Includes bibliographical references
Rights
© 1998 Ananda Amarasekara Jayawardhana, All rights reserved.
Document Type
Dissertation - Restricted Access
File Type
text
Language
English
Thesis Number
T 7570
Print OCLC #
41450084
Recommended Citation
Jayawardhana, Ananda, "Predictive density estimation in life testing" (1998). Doctoral Dissertations. 1286.
https://scholarsmine.mst.edu/doctoral_dissertations/1286
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