Faculty
Department of Statistical and Actuarial Sciences
Supervisor Name
Serge B. Provost
Keywords
q-distributions; maximum likelihood estimation; data modeling; method of moments; quadratic forms.
Description
This project introduces a flexible univariate probability model referred to as the q-analogue of the Extended Generalized Gamma (or q-EGG) distribution, which encompasses the majority of the most frequently used continuous distributions, including the gamma, Weibull, logistic, type-1 and type-2 beta, Gaussian, Cauchy, Student-t and F. Closed form representations of its moments and cumulative distribution function are provided. Additionally, computational techniques are proposed for determining estimates of its parameters. Both the method of moments and the maximum likelihood approach are utilized. The effect of each parameter is also graphically illustrated. Certain data sets are modeled with q-EGG distributions; goodness of fit is assessed by making use of the Anderson–Darling and Cram´er–von Mises criteria, among others. Improved approximations to the distribution of quadratic forms are considered as well. Since much effort was expended to develop the code required to implement the various methodologie
Acknowledgements
Thank you to Dr. Provost, the URSI program, and the Department of Statistical and Actuarial Sciences for their support.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Document Type
Paper
Included in
Applied Statistics Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons
The q-Analogue of the Extended Generalized Gamma Distribution
This project introduces a flexible univariate probability model referred to as the q-analogue of the Extended Generalized Gamma (or q-EGG) distribution, which encompasses the majority of the most frequently used continuous distributions, including the gamma, Weibull, logistic, type-1 and type-2 beta, Gaussian, Cauchy, Student-t and F. Closed form representations of its moments and cumulative distribution function are provided. Additionally, computational techniques are proposed for determining estimates of its parameters. Both the method of moments and the maximum likelihood approach are utilized. The effect of each parameter is also graphically illustrated. Certain data sets are modeled with q-EGG distributions; goodness of fit is assessed by making use of the Anderson–Darling and Cram´er–von Mises criteria, among others. Improved approximations to the distribution of quadratic forms are considered as well. Since much effort was expended to develop the code required to implement the various methodologie