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APPLICATION OF STATISTICAL METHODS IN RISK AND RELIABILITY

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Date Issued:
2005
Abstract/Description:
The dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures. The confidence intervals are constructed by objective Bayesian methods and use the Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations and compared to the performance of nonparametric confidence intervals based on binomial proportion. In addition, techniques for change point detection are analyzed and further evaluated via Monte Carlo simulations. The effect of a change point on the interval estimators is studied both analytically and via Monte Carlo simulations.
Title: APPLICATION OF STATISTICAL METHODS IN RISK AND RELIABILITY.
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Name(s): Heard, Astrid, Author
Pensky, Marianna, Committee Chair
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2005
Publisher: University of Central Florida
Language(s): English
Abstract/Description: The dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures. The confidence intervals are constructed by objective Bayesian methods and use the Jeffreys noninformative prior. Performance of the resulting confidence intervals is studied via Monte Carlo simulations and compared to the performance of nonparametric confidence intervals based on binomial proportion. In addition, techniques for change point detection are analyzed and further evaluated via Monte Carlo simulations. The effect of a change point on the interval estimators is studied both analytically and via Monte Carlo simulations.
Identifier: CFE0000736 (IID), ucf:46565 (fedora)
Note(s): 2005-12-01
Ph.D.
Arts and Sciences, Department of Mathematics
Doctorate
This record was generated from author submitted information.
Subject(s): Confidence Intervals
Bayes
cumulative distribution functions
quantiles
small sample size
Generalized Gamma Distribution
Jeffreys Prior Distribution
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0000736
Restrictions on Access: public
Host Institution: UCF

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