Topics Involving the Gamma Distribution: the Normal Coefficient of Variation and Conditional Monte Carlo.

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dc.contributor.advisor William Swallow, Committee Chair en_US
dc.contributor.advisor Dennis Boos, Committee Member en_US
dc.contributor.advisor Cavell Brownie, Committee Member en_US
dc.contributor.advisor Thomas Gerig, Committee Member en_US
dc.contributor.advisor Michael Boyette, Committee Member en_US Boyer, Joseph Guenther en_US 2010-04-02T18:35:17Z 2010-04-02T18:35:17Z 2007-01-19 en_US
dc.identifier.other etd-12102006-182537 en_US
dc.description.abstract A transformation of the sample coefficient of variation ($CV$) for normal data is shown to be nearly proportional to a $chiˆ2$ random variable. The associated density is applied to inference on the common $CV$ of $k$ populations, testing $CV$ homogeneity across populations, and confidence intervals for the ratio of two $CV$s. The resulting tests and confidence intervals are shown via theory and simulation to be valid and powerful. In other work on the coefficient of variation, a sample of scientific abstracts is used to characterize the values of the $CV$ encountered in practice, point estimation for a common $CV$ in normal populations is studied, and the literature on testing $CV$ homogeneity in normal populations is reviewed. There is very little literature on the problem of conducting inference in models for continuous data conditional on sufficient statistics for nuisance parameters. This thesis explores Monte Carlo approaches to conditional $p$-value calculation in such models, including Dirichlet data generation, importance sampling, Markov chain Monte Carlo, and a method related to fiducial inference. Importance sampling is used to create a conditional test of $CV$ homogeneity in normal populations using the $chi^2$ approximation mentioned above. A Markov chain Monte Carlo solution is given to the long-standing problem of testing the homogeneity of exponential populations subject to Type I censoring. Conditional Monte Carlo algorithms are also applied to testing for an effect of a factor in an experiment with exponential data, testing for a dispersion effect in a replicated experiment with normal data, and testing a null value of a coefficient in exponential regression with an inverse link; brief consideration is also given to the problem of testing the homogeneity of $k$ $gamma$ distributions. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject exponential distribution en_US
dc.subject dispersion effects en_US
dc.subject Jacobian en_US
dc.subject Type I censoring en_US
dc.subject exponential regression en_US
dc.subject Gibbs sampling en_US
dc.subject Dirichlet distribution en_US
dc.subject importance sampling en_US
dc.subject conditional Monte Carlo en_US
dc.subject nuisance parameters en_US
dc.subject conditional inference en_US
dc.subject sufficient statistic en_US
dc.subject coefficient of variation en_US
dc.subject exponential family en_US
dc.subject gamma distribution en_US
dc.title Topics Involving the Gamma Distribution: the Normal Coefficient of Variation and Conditional Monte Carlo. en_US PhD en_US dissertation en_US Statistics en_US

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