KUMARASWAMY TYPE II GENERALIZED TOPP-LEONE-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS

Abstract

In the field of reliability theory, practitioners have been working assiduously in recent years to propose new families of continuous probability distributions that extend the standard theoretical distribution that is currently in use. They have done this by hybridizing two or more probability models or by introducing one or more parameters to get more flexibility in fitting data from a variety of fields, including the environmental, economics, finance, and medical sciences. The T-X approach was used to establish the Kumaraswamy Type II Generalized Topp-Leone-G (K_wT₂GTL-G) family, which extends the Type II Generalized Topp-Leone-G family of distributions with extra shape parameters. A few statistical characteristics of the novel family were determined and examined. A sub-model emerged and MLE was used to estimate the model parameters. To demonstrate the value of the new family, two real-life data sets were used: a set that related to the relief times (in minutes) of patients taking an analgesic, and the other that related to the failure and service times for a windshield. The superior goodness-of-fits and empirical flexibility of the K_wT₂GTL-G distribution are demonstrated by comparisons with other distributions, including the Kumaraswamy Extension Exponential (K_wEEx), Kumaraswamy Exponential (KEx), Exponential Generalized Exponentiated Exponential (EGEEx), and Exponentiated Weibull-Exponential (EWEx) distributions.. In the second dataset, the K_wT₂GTLEx distribution achieved an AIC value of 38.0489, outperforming the EGEEx distribution which had an AIC value of 39.6708 next to it. These findings highlight the K_wT₂GTL-G family's potential to enhance lifetime data modeling, which would have a substantial impact on engineering,...