On the exponentiated Type II Generalized Topp-Leone-G Family of distribution: properties and applications

Abstract

In the modern era of statistics, distribution theory plays a crucial role in accurately modelling phenomena across various scientific fields. Traditional statistical distributions often fall short of adequately representing complex lifetime data. To address this limitation, this study introduces the Exponentiated Type II Generalized Topp-Leone-G (ET2GTL-G) family of distributions. This study employs the maximum likelihood estimation (MLE) method to estimate the parameters of the ET2GTL-G family and illustrates its application to two real-life datasets: (1) civil engineering hailing times, and (2) failure and service times for a windshield. Comparative analyses with existing distributions, such as the Kumaraswamy Extension Exponential (KEED), Kumaraswamy Exponential (KED), Exponential Generalized Exponentiated Exponential (EGEE), and Exponentiated Weibull-Exponential (EWED) distributions, highlight the superior goodness-of-fit and empirical flexibility of the ET2GTL-G distribution. For the first dataset, the ET2GTL-G distribution reported a minimum Akaike Information Criterion (AIC) value of 274.7174, compared to the next best-fit KED with an AIC value of 275.0377. For the second dataset, the ET2GTL-G distribution achieved an AIC value of 204.2458, outperforming the EGEE distribution which had an AIC value of 206.9956. These results underscore the potential of the ET2GTL-G family to improve the modelling of lifetime data, thereby contributing significantly to the fields of medicine, engineering, and beyond.