The McDonald Weibull model

Abstract

For the first time, we propose a five-parameter lifetime model called the McDonald Weibull distribution to extend the Weibull, exponentiated Weibull, beta Weibull and Kumaraswamy Weibull distributions, among several other models. We obtain explicit expressions for the ordinary moments, quantile and generating functions, mean deviations and moments of the order statistics. We use the method of maximum likelihood to fit the new distribution and determine the observed information matrix. We define the log-McDonald Weibull regression model for censored data. The potentiality of the new model is illustrated by means of two real data sets.

Keywords:

• Kumaraswamy distribution
• maximum-likelihood estimation
• McDonald distribution
• mean deviation
• moment generating function
• quantile function
• Weibull distribution

Acknowledgements

This work was supported by FAPESP grant 2010/04496-2 and CNPq, Brazil. We thank the two referees and the editor for very helpful comments.

Notes

1. http://functions.wolfram.com/06.23.06.0004.01.