A new method for generating distributions with an application to exponential distribution

ABSTRACT

A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility. A special case has been considered in detail, namely one-parameter exponential distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment-generating function, mean residual lifetime, stochastic orders, order statistics, and expression of the entropies, are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non linear equations only. Further, we consider an extension of the two-parameter exponential distribution also, mainly for data analysis purposes. Two datasets have been analyzed to show how the proposed models work in practice.

KEYWORDS:

• Fisher information matrix
• Exponential distribution
• Hazard rate function
• Maximum likelihood estimation
• Survival function

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62E15
• Secondary: 62H10

Acknowledgments

The authors would like to thank the associate editor and two referees for their constructive comments.