Development and Applications of the Type II Half-Logistic Inverse Weibull Distribution

Abstract

A variety of distribution classes have emerged by expanding or generalizing well-known continuous distributions to enhance their flexibility and adaptability across various fields. One such distribution is the Inverse Weibull (IW) distribution, introduced by Keller and Kanath in 1982, which has proven effective in modelling failure characteristics. Over the years, several extensions of the IW distribution have been developed, including the Beta Inverse Weibull, Kumaraswamy-Inverse Weibull, and many others. This paper introduces a novel extension called the Type II Half-Logistic Inverse Weibull (TIIHLEtIW) distribution, derived from the Type II Half-Logistic Exponentiated-G (TIIHLEt-G) family proposed by Bello et al. in 2021. The TIIHLEtIW distribution incorporates two additional shape parameters, enhancing its flexibility. We provide the cumulative distribution function (cdf), probability density function (pdf), and key statistical properties, including moments, moment-generating function, reliability function, hazard function, and quantile function. Maximum likelihood estimation (MLE) is employed for parameter estimation, and a simulation study evaluates the performance of the MLEs. Finally, the applicability and superiority of the TIIHLEtIW distribution are demonstrated through a comparative study using two real datasets, showcasing its improved fit over several established distributions.