A modified exponentiated inverted Weibull distribution using Modi family

Abstract

This paper proposes a new extension of the Exponentiated Inverted Weibull distribution using the Modi Family, called the Modi Exponentiated Inverted Weibull (MEIW) distribution that adds an extra shape parameter, allowing for a wider range of shapes for failure rates. Mathematical properties were developed, including hazard rate, survival function, reversed hazard rate, quantile function, moments, order statistics, and Renyi Entropy. Maximum Likelihood Estimation is employed for parameter estimation, with the performance of the estimators assessed through Monte Carlo simulation. The new distribution is fitted to the two real data sets and compared with some existing distributions such as Exponentiated Inverted Weibull (EIW), Inverse Weibull (IW), and Weibull (WE) distributions. The goodness-of-fit statistics and information criteria values demonstrated that the new distribution fits better the two real data sets than the other distributions.