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APPLICATION OF STATISTICAL METHODS IN RISK AND RELIABILITY
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TitleAPPLICATION OF STATISTICAL METHODS IN RISK AND RELIABILITY
AuthorHeard, Astrid
KeywordsConfidence Intervals
Bayes
cumulative distribution functions
quantiles
small sample size
Generalized Gamma Distribution
Jeffreys Prior Distribution
AbstractThe 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.
AdviserPensky, Marianna
PublisherUniversity of Central Florida
DegreePh.D.
Degree DisciplineDepartment of Mathematics
Degree GrantorArts and Sciences
Degree ProgramMathematics
Graduation Date2005-12-01
TypeDoctoral dissertation
Access LevelPublic - Allow Worldwide Access
Release Date2006-01-09
RepositoryUniversity Archives
Repository CollectionElectronic Theses and Dissertations
IdentifierCFE0000736
Access Linkhttp://purl.fcla.edu/fcla/etd/CFE0000736

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