G Families of Probability Distributions

Theory and Practices

Mir Masoom Ali, Irfan Ali, Haitham M. Yousof, Mohamed Ibrahim Mohamed Ahmed, Mir Masoom Ali, Irfan Ali, Haitham M. Yousof, Mohamed Ibrahim Mohamed Ahmed

• Publisher: CRC Press
• Year: 2023
• Print ISBN:
  9781032140650
• eBook ISBN:
  9781000860412
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover
• Title
• Copyright
• Preface
• Acknowledgement
• Contents
• 1. A New Compound G Family of Distributions: Properties, Copulas, Characterizations, Real Data Applications with Different Methods of Estimation
• 2. A Novel Family of Continuous Distributions: Properties, Characterizations, Statistical Modeling and Different Estimation Methods
• 3. On the use of Copulas to Construct Univariate Generalized Families of Continuous Distributions
• 4. A Family of Continuous Probability Distributions: Theory, Characterizations, Properties and Different Copulas
• 5. New Odd Log-Logistic Family of Distributions: Properties, Regression Models and Applications
• 6. On the Family of Generalized Topp-Leone Arcsin Distributions
• 7. The Truncated Modified Lindley Generated Family of Distributions
• 8. An Extension of the Weibull Distribution via Alpha Logarithmic G Family with Associated Quantile Regression Modeling and Applications
• 9. The Topp-Leone-G Power Series Distribution: Its Properties and Applications
• 10. Exponentiated Generalized General Class of Inverted Distributions: Estimation and Prediction
• 11. A New Class of Discrete Distribution Arising as an Analogue of Gamma-Lomax Distribution: Properties and Applications
• 12. New Compounding Lifetime Distributions with Application to Hard Drive Reliability
• 13. Comparing the Performance of G-family Probability Distribution for Modeling Rainfall Data
• 14. Record-Based Transmuted Kumaraswamy Generalized Family of Distributions: Properties and Application
• 15. Finding an Efficient Distribution to Analyze Lifetime Data through Simulation Study
• 16. Exponentiated Muth Distribution: Properties and Applications
• 17. Exponentiated Discrete Modified Lindley Distribution and its Applications in the Healthcare Sector
• 18. Length Biased Weighted New Quasi Lindley Distribution: Statistical Properties and Applications
• 19. A New Alpha Power Transformed Weibull Distribution: Properties and Applications
• 20. An Extension of Topp-Leone Distribution with Increasing, Decreasing and Bathtub Hazard Functions
• 21. Testing the Goodness of Fit in Instrumental Variables Models
• 22. Probability Distribution Analysis for Rainfall Scenarios—A Case Study
• Index