Arctan Inverse Weibull Distribution: Estimation, Simulation and Application

Abstract

In this study, we introduce the arctan inverse Weibull (AIW) distribution, which is an extension of the inverse Weibull (IW) distribution. The AIW distribution is more flexible than other well-known statistical models, and it includes several sub-models. We computed the AIW distribution's statistical features such as quantile function, median, skewness, kurtosis, inverse moments, harmonic mean (HM) and order statistics. The model parameters were determined using the maximum likelihood (ML) approach. A Monte Carlo simulation study is described to evaluate the effectiveness of the ML technique for calculating AIW distribution parameters. To demonstrate the significance of the AIW distribution, we implemented it to an actual dataset of current interest: COVID-19 death cases recorded in the Kingdom of Saudi Arabia (KSA) from 14 April to 22 June 2020. The new suggested model gives better fit more than other competitive models for the dataset.