Some New Transformed and Generalized Families of Distributions with Applications

Abstract

This thesis presents several new generalized classes and families of distributions, namely, the log-logistic modified Weibull power series (LLoGMWPS) class of distributions, type II Topp-Leone exponentiated half logistic-G power series (TII-TL-EHL-GPS) class of distributions, Harris-odd Burr type X-G (Harris-OBX-G) family of distributions, Marshall-Olkin Exponentiated Half Logistic-Type II Topp-Leone-G (MO-EHL-TII-TL-G) family of distributions, and Topp-Leone Harris-G (TL-Harris-G) family of distributions. These classes and families of distributions are developed using different combinations of generators and existing distributions. The mathematical and statistical properties of these new classes and families of distributions, including moments and moment generating functions, distribution of order statistics, probability weighted moments, and R´enyi entropy, are derived and thoroughly examined. Additionally, the identifiability issue, concerning whether the parameters of the proposed models can be uniquely determined from observed data is investigated using mathematical functions for each class of distributions and family of distributions. Finally, the flexibility and applicability of these new classes and families of distributions are demonstrated by fitting them to various real datasets. Several goodness-of-ft statistics and graphical plots are utilized to assess the adequacy of the models in capturing the complex characteristics of datasets across different domains.