Some parsimonious models for lifetimes and applications
P. Kavya, M. Manoharan
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.