Keywords

Confidence Intervals, Bayes, cumulative distribution functions, quantiles, small sample size, Generalized Gamma Distribution, Jeffreys Prior Distribution

Abstract

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.

Notes

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Graduation Date

2005

Semester

Fall

Advisor

Pensky, Marianna

Degree

Doctor of Philosophy (Ph.D.)

College

College of Arts and Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0000736

URL

http://purl.fcla.edu/fcla/etd/CFE0000736

Language

English

Release Date

January 2006

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

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Included in

Mathematics Commons

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