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.
Statistical distributions are important tools to model the characteristics of data sets observed in different applied sciences such as engineering, medicine, and finance, among others. This book will help future and current researchers in the field of G families of probability distributions.
A New Compound G Family of Distributions: Properties, Copulas,
Characterizations, Real Data Applications with Different Methods of
Estimation. A Novel Family of Continuous Distributions: Properties,
Characterizations, Statistical Modeling and Different Estimation Methods. On
the use of Copulas to Construct Univariate Generalized Families of Continuous
Distributions. A Family of Continuous Probability Distributions: Theory,
Characterizations, Properties and Different Copulas. New Odd Log-Logistic
Family of Distributions: Properties, Regression Models and Applications. On
the Family of Generalized Topp-Leone Arcsin Distributions. The Truncated
Modified Lindley Generated Family of Distributions. An extension of the
Weibull distribution via Alpha logarithmic G family with Associated Quantile
Regression Modeling and Applications. The Topp-Leone-G Power Series
Distribution: Its Properties and Applications. Exponentiated Generalized
General Class of Inverted Distributions: Estimation and Prediction. A New
Class of Discrete Distribution Arising as an Analogue of Gamma-Lomax
Distribution: Properties and Applications. New Compounding Lifetime
Distributions with Application to Hard Drive Reliability. Comparing the
Performance of G-Family Probability Distribution for Modeling Rainfall Data.
Record-Based Transmuted Kumaraswamy Generalized Family of Distributions.
Finding an Efficient Distribution to Analyze Lifetime Data through Simulation
Study. Exponentiated Muth Distribution: Properties and Applications.
Exponentiated Discrete Modified Lindley Distribution and its Applications in
Healthcare Sector. Length Biased Weighted New Quasi Lindley Distribution:
Statistical Properties and Applications. A New Alpha Power Transformed
Weibull Distribution: Properties and Applications. An Extension of Topp-Leone
Distribution with Increasing, Decreasing and Bathtub Hazard Functions.
Goodness of Fit Test in Instrumental Variables Models. Probability
Distribution Analysis for Rainfall Scenarios A Case Study.
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.
