Some parsimonious models for lifetimes and applications

Abstract

The principle of parsimonious modelling of lifetimes has regained its importance recently. The value of stochastic modelling in dealing with the inevitable uncertainty and risk is nowadays highly appreciated. However, several families of distributions used in stochastic modelling of lifetimes are often non-parsimonious, unnatural, theoretically unjustified, and sometimes unnecessary. Here we propose a transformation for obtaining a new class of parsimonious distributions, and introduce two new distributions using exponential and Weibull as the baseline distribution in this transformation. The behaviour of hazard rates of the distributions are examined along with other analytical properties. Parameter estimation of the proposed models is done using the maximum likelihood method. Using simulation studies, we have shown that the parameters estimated from the distributions are consistent. Further, the new parsimonious life distributions are applied to a real data set. Our models provide a better fit to the data compared to various distributions in the literature.

Keywords:

• Parsimonious model
• lifetime
• KM transformation
• exponential distribution
• Weibull distribution

Acknowledgments

The authors wish to acknowledge the anonymous referee and associate editor for the critical comments and suggestions which helped us improve the manuscript considerably.

Disclosure statement

No potential conflict of interest was reported by the author(s).