Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Statistics and Actuarial Sciences

Supervisor

Serge B. Provost

Abstract

We introduce a generalized exponential model whose exact moments and normalizing constant are obtained in terms of Meijer’s generalized hypergeometric G-function. Actually, several widely utilized statistical distributions such as the gamma, Weibull and half-normal constitute particular cases thereof. The generalized inverse Gaussian distribution, which was popularized in the late seventies by Ole Barndor_Neilsen, is also extended by incorporating an additional parameter in its density function, the moments of the resulting distribution being expressed in terms of Bessel functions. A number of data sets were then fitted with diverse exponential-type models for comparison purposes. Additionally, it is shown that the inverse Mellin transform technique may be employed to derive a multiple series representation of the density function of linear combinations of chi-square random variables, which are encountered for instance in connection with the distribution of certain quadratic forms and some asymptotic distributional results arising in multivariate analysis. The accuracy of the truncated form of this density function is compared to that obtained from a reparameterized generalized gamma distribution. A methodology whereby regression problems are converted into density estimation problems is also proposed and applied to certain actuarial data sets. A technique for modeling bivariate observations is presented as well.

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