Statistics and Probability Commons^™

Generalized Exponential Models With Applications, Iman Mabrouk

Electronic Thesis and Dissertation Repository

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 …