The McDonald Extended Weibull Distribution

Abstract

Generalizing lifetime distributions is always precious for statisticians. We propose and study a new six-parameters lifetime distribution called the McDonald extended Weibull model to generalize the Weibull, extended Weibull, exponentiated Weibull, Kumaraswamy Weibull, Kumaraswamy exponential, beta Weibull, beta exponential, and McDonald extended exponential, among several others. We obtain explicit expressions for the moments, incomplete moments, generating and quantile functions, mean deviations, and Bonferroni and Lorenz curves. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The potentiality of the new model is illustrated by means of a real data set.

AMS Subject Classification:

• 62N01
• 62N02

Keywords:

• Exponentiated Weibull distribution
• Generating function
• Maximum likelihood estimation
• McDonald distribution
• Mean deviation
• Quantile function