On MLEs of the parameters of a modified Weibull distribution based on record values

ABSTRACT

The modified Weibull distribution can be used quite effectively to model complex data from mechanical engineering or survival analysis studies that posses a monotonic or a bathtub-shape hazard rate. In this paper, we study the MLEs of the parameters of a modified Weibull distribution model in the presence of upper kth record values. The existence and uniqueness of the MLEs are proven in this case. Real data analysis is performed for illustrative purposes.

KEYWORDS:

• Modified Weibull distribution
• records
• Hessian matrix
• uniqueness and existence

Acknowledgments

The author would like to thank the referees for their valuable comments and suggestions that significantly improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.