On some aspects of a flexible class of additive Weibull distribution

ABSTRACT

Here we consider a more flexible class of the additive Weibull distribution of Xie and Lai (Reliab. Eng. Syst. Safety, 1995) and investigate some of its important properties such as expressions for its cumulative distribution function, reliability measures, quantile function, characteristic function, raw moments, incomplete moments, etc. The distribution and moments of order statistics are obtained along with certain structural properties. The maximum-likelihood estimation of the parameters of the distribution is attempted and the usefulness of the model in certain applied areas is illustrated with the help of certain real life data sets.

KEYWORDS:

• Hazard rate
• maximum-likelihood estimation
• model selection
• order statistics
• reliability measures
• simulation.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 60E10

Acknowledgments

The authors would like to express their sincere thanks to the Chief Editor, the Associate Editor, and all the three anonymous referees for their valuable comments on an earlier version of the paper, which greatly improved the quality and presentation of the manuscript.