Parameter estimation of the four-parameter Harris extended Weibull distribution with applications to real-life data

Abstract

This paper explores the extension of the classical two-parameter Weibull distribution to a four-parameter Harris extended Weibull (HEW) distribution. The flexibility of this probability distribution is illustrated by the varying shapes of HEW density function. Estimation of HEW parameters is explored using estimation methods such as the least-squares, maximum product of spacings, and minimum distance method. We provide Bayesian inference on the random parameters of the HEW distribution using Metropolis-Hastings algorithm to sample from the joint posterior distribution. Performance of the estimation methods is assessed using extensive simulations. The applicability of the distribution is demonstrated against three variants of the Weibull distribution on three real-life datasets.