Development of new generalized families of distributions via multiple generators with applications

Abstract

Complex real life phenomena requires robust statistical and mathematical tools that can capture and incorporate many statistical aspects of the processes or events under study with a high degree of accuracy and precision. Classical and other existing probability distributions in literature have some shortcomings when it comes to capturing the characteristics of various data sets, they su↵er lack of flexibility hence poor performance when modelling data sets with di↵erent types of the hazard rate functions: decreasing, increasing, bathtub, upside-down bathtub and also di↵erent levels of skewness and kurtosis as often exhibited by many data sets in real life. In light of the above, we proposed and developed several new generalized families of distributions via new and multiple combinations of generators. We developed the Exponentiated Half Logistic-Weibull-Topp-Leone-G family of distributions, the Weibull-Topp-Leone-G power series class of distributions, the Exponentiated Half Logistic-Type II Topp-Leone-G family of distributions, the Marshall-Olkin-Topp-Leone Half Logistic-G family of distributions, the Marshall-Olkin-Generalized Exponentiated Half Logistic-G family of distributions, the MarshallOlkin-Odd Exponential Topp-Leone-G family of distributions and the Burr III-Exponentiated Half Logistic-G family of distributions. The use of combinations of multiple generators enabled us to generate new families of distributions which have a strong capacity to handle or capture the important characteristics (skewness and kurtosis) of data thereby adding the much needed flexibility in many applied areas. Mathematical and statistical properties of these generalized distributions including series expansion of probability density functions, hazard rate functions, quantile functions, moments, conditional moments, probability weighted moments, stochastic orders, R´enyi entropy and distribution of order statistics are presented. Monte-Carlo simulation algorithms were developed for the new families of distributions. We used the maximum likelihood estimation technique to estimate parameters of our models. We assessed the consistency of our estimators via Monte-Carlo simulations. Applications to real life data have been used to demonstrate the applicability of the new generalized families of distributions. This work will help practitioners in various fields of study to make more accurate decisions.