1st Edition

G Families of Probability Distributions Theory and Practices

    364 Pages 101 B/W Illustrations
    by CRC Press

    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.

    A New Compound G Family of Distributions: Properties, Copulas, Characterizations, Real Data Applications with Different Methods of Estimation

    M. Masoom Ali, Nadeem Shafique Butt, G.G. Hamedani, Saralees Nadarajah, Haitham M. Yousof, Mohamed Ibrahim

    A Novel Family of Continuous Distributions: Properties, Characterizations, Statistical Modeling and Different Estimation Methods

    Haitham M. Yousof, M. Masoom Ali, Gauss M. Cordeiro, G.G. Hamedani and Mohamed Ibrahim

    On the use of Copulas to Construct Univariate Generalized Families of Continuous Distributions

    Christophe Chesneau and Haitham M. Yousof

    A Family of Continuous Probability Distributions: Theory, Characterizations, Properties and Different Copulas

    Mohammad Mehdi Saber, G.G. Hamedani, Haitham M. Yousof, Nadeem Shafique Butt, Basma Ahmed and Mohamed Ibrahim

    New Odd Log-Logistic Family of Distributions: Properties, Regression Models and Applications

    Emrah Altun, MoradAlizadeh, GamzeOzel and Haitham M. Yousof

    On the Family of Generalized Topp-Leone Arcsin Distributions

    Vikas Kumar Sharma, Komal Shekhawat and Sanjay Kumar Singh

    The Truncated Modified Lindley Generated Family of Distributions

    Lishamol Tomy, Christophe Chesneau and Jiju Gillariose

    An extension of the Weibull distribution via Alpha logarithmic G family with Associated Quantile Regression Modeling and Applications

    Yunus Akdoğan, Kadir Karakaya, Mustafa Ç. Korkmaz, Fatih Şahin, Aşır Genç

    The Topp-Leone-G Power Series Distribution: Its Properties and Applications

    Laba Handique, Subrata Chakraborty and M. Masoom Ali

    Exponentiated Generalized General Class of Inverted Distributions: Estimation and Prediction

    Abeer A. EL-Helbawy, Gannat R. AL-Dayian, Asmaa M. Abd AL-Fattah and Rabab E. Abd EL-Kader

    A New Class of Discrete Distribution Arising as an Analogue of Gamma-Lomax Distribution: Properties and Applications

    Indranil Ghosh, Ayman Alzaatreh, G.G. Hamedani

    New Compounding Lifetime Distributions with Application to Hard Drive Reliability

    A. Asgharzadeh, Hassan S. Bakouch, L. Esmaeili, S. Nadarajah

    Comparing the Performance of G-Family Probability Distribution for Modeling Rainfall Data

    Md. Mostafizur Rahman, Md. Abdul Khalek and M. Sayedur Rahman

    Record-Based Transmuted Kumaraswamy Generalized Family of Distributions

    Qazi J. Azhad, Mohd. Arshad, Bhagwati Devi, Nancy Khandelwal, and Irfan Ali

    Finding an Efficient Distribution to Analyze Lifetime Data through Simulation Study

    Anamul Haque Sajib, Trishna Saha and M Sayedur Rahman

    Exponentiated Muth Distribution: Properties and Applications

    R. Maya, M.R. Irshad, Anuresha Krishna

    Exponentiated Discrete Modified Lindley Distribution and its Applications in Healthcare Sector

    Lishamol Tomy, Veena G and Christophe Chesneau

    Length Biased Weighted New Quasi Lindley Distribution: Statistical Properties and Applications

    Aafaq A. Rather

    A New Alpha Power Transformed Weibull Distribution: Properties and Applications

    Ashok Kumar Pathak, Mohd. Arshad, Sanjeev Bakshic and Mukti Khetan

    An Extension of Topp-Leone Distribution with Increasing, Decreasing and Bathtub Hazard Functions

    Unnati Nigam and Arun Kaushik

    Goodness of Fit Test in Instrumental Variables Models

    Shalabh and Subhra Sankar Dhar

    Probability Distribution Analysis for Rainfall Scenarios – A Case Study

    Md. Abdul Khalek, Md. Mostafizur Rahaman, Md. Kamruzzaman, Md. Mesbahul Alam and M. Sayedur Rahman


    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.