CONTRIBUTIONS TO DISTRIBUTION THEORY WITH APPLICATIONS

Abstract

The whole thesis contains 4 chapters. Chapter 1 is the introductory chapter of my thesis and the main contributions are in Chapter 2 through to Chapter 4. The theme of these chapters is developing and reviewing statistical distributions. Bhati and Ravi [Insurance: Mathematics and Economics, 79, 2018, 247-259] introduced a new heavy tailed distribution referred to as the generalized log-Moyal distribution. Chapter 2 points out that: i) this distribution is a particular case of many known distributions; ii) the two data sets considered can be fitted better by known distributions, with differences in AIC exceeding 60 and differences in BIC exceeding 50; iii) this distribution does not provide an adequate fit for one of the data sets while known distributions do. A recent paper introduced a new distribution referred to as the inverse Nakagami-m distribution. Chapter 3 points out that this distribution is a particular case of many known distributions. It also shows that four data sets can be fitted better by known distributions, with differences in information criteria exceeding 20. The better fits are justified also using three goodness of fit tests. Chapter 4 introduces A new class of distributions motivated by systems having both series and parallel structures. Some mathematical properties of the new class (including the moment generating function, moments and order statistics) are derived. Estimation is addressed by the maximum likelihood method and the performance of the estimators assessed by a simulation study. An illustration using three failure data sets shows the usefulness of the new class.

Date of Award	1 Aug 2020
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Peter Foster (Supervisor) & Saraleesan Nadarajah (Supervisor)