A New Modification of Shanker Distribution with Applications to Increasing Failure Rate Data

Abstract

In this paper, a new distribution is proposed by mixing the exponential distribution and the Shanker distribution with a mixing proportion being the same as those that yielded the Shanker distribution. The proposed distribution is referred to as the XShanker distribution. The distributional properties of the XShanker distribution namely, quantile function, moments and their associated measures,the mode, moment generating function, characteristic function, distribution of order statistics, and entropy are derived and studied. The reliability analysis shows that the failure rate is a strictly increasing function. The parameter of the model was estimated using the maximum likelihood function. We illustrated the usefulness of XShanker distribution using data on waiting times of 100 bank customers and vinyl chloride from clean ungradient ground-water monitoring wells in (g/L).