G Families of Probability Distributions : Theory and Practices

Statistical distributions are essential tools to model the characteristics of datasets, such as right or left skewness, bi-modality or multi-modality observed in different applied sciences, such as engineering, medicine, and finance. The well-known distributions like normal, Weibull, gamma and Lindley are extensively used because of their simple forms and identifiability properties. In the last decade, researchers have focused on the more complex and flexible distributions, referred to as Generalized or simply G families of probability distributions, to increase the modelling capability of these distributions by adding one or more shape parameters.

The main aim of this edited book is to present new contributions by researchers in the field of G families of probability distributions. The book will help researchers to:

• Develop new univariate continuous and discrete G families of probability distributions.
• Develop new bivariate continuous and discrete G families of probability distributions.
• Derive beneficial mathematical properties such as ordinary and incomplete moments, moment generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering and entropies, and some bivariate and multivariate extensions of the new and existing models using a simple-type copula.

Dr. Mir Masoom Ali is George and Frances Ball Distinguished Professor Emeritus of Statistics at Ball State University in the USA. His current research interest is in the area of G Families of probability distributions and he has published numerous papers in this area.

Dr. Irfan Ali is an Assistant Professor of Statistics at the Department of Statistics and Operations Research, Aligarh Muslim University, India. His current research areas are applied statistics and mathematical programming and he has published more than 100 research papers in these areas.

Dr. Haitham M. Yousof is an Assistant professor of Statistics at the Department of Statistics, Mathematics and Insurance, Benha University, Egypt. His current research areas are probability theory and G Families of probability distributions and he has published more than 200 research papers in these areas.

Dr. Mohamed Ibrahim is an Assistant professor of Statistics at the Department of Applied, Mathematical and Actuarial Statistics, Damietta University, Egypt. His current research areas are probability theory and G Families of probability distributions and he has published several research papers in these areas.