A New Flexible Generalized Distribution: The Modified Kies Inverse Weibull Distribution with Properties, Estimations and Applications

Abstract

This study introduces the Modified Kies Inverse Weibull (MKIW) distribution as a new generalisation of the Inverse Weibull (IW) distribution within the Modified Kies-G family of distributions. The proposed model extends existing IW generalisations through an odds-based exponential generator, thereby providing enhanced flexibility in modelling skewness, tail behaviour, and hazard rate structures. Several structural and statistical properties of the distribution are derived, including the quantile function, moments, skewness, kurtosis, median, mode, order statistics, and reliability measures. Parameter estimation is investigated using six estimation methods. A Monte Carlo simulation study is conducted to assess the performance of the estimators in terms of average bias, average absolute bias, mean relative error, standard deviation, and mean squared error. The results indicate that the maximum product of spacings and maximum likelihood methods provide the most efficient estimators across most parameter settings. The practical applicability of the MKIW distribution is illustrated using four real lifetime datasets. Comparative analyses show that the proposed model provides a competitive fit relative to the classical IW distribution and several of its extensions, including the exponentiated generalised, Kumaraswamy, Topp-Leone, and alpha power IW distributions. In particular, the MKIW distribution reduces the AIC by approximately 4.2% to 16.5% when compared with the classical IW model across the four datasets, demonstrating its flexibility and usefulness for modelling complex lifetime data.