Topics Involving the Gamma Distribution: the Normal Coefficient of Variation and Conditional Monte Carlo.
Year: 2007
Type: article
Abstract: Involving the Gamma Distribution: The Normal Coefficient of Variation and Conditional Monte Carlo.(Under the direction of William H. Swallow).A transformation of the sample coefficient of variation (CV ) for normal data is shown to be nearly proportional to a χ 2 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 χ 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. DedicationTo Lori, for making me finish.To Ellen, my kindred spirit.We continue to overcome.And to Monahan's prisoners, all current and future, for the fight that cannot be won, but not being fought cannot be lost, for the lock that cannot be broken but is not fastened, and for the journey that no perseverance can ever end, but that can be simply ended, by the power within you that courage shall unleash to turn the hand upon the doorknob, open to an anticlimactic day.
Author: Joseph Boyer
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2522389412