Rani Distribution and Its Application

Abstract

In the present paper, a new one parameter lifetime distribution named, “Rani Distribution’ has been proposed for modeling lifetime data from engineering and biomedical sciences. Its various statistical and mathematical properties including its shapes for varying values of parameter, moments and moments based measures, hazard rate function, mean residual life function, stochastic ordering, deviations from the mean and the median, Bonferroni and Lorenz curves, order statistics , Renyi entropy measure and stress-strength reliability have been studied. Both the maximum likelihood estimation and the method of moments have been discussed for estimating the parameter of the proposed distribution. A simulation study has been carried out and results are presented. A numerical example has been presented to test the goodness of fit of the proposed distribution and it has been found that it gives much closer fit than almost all one parameter lifetime distributions introduced in statistical literature.