Inverted Weibull Poisson Distribution: Properties, Inference and Applications to Engineering Data

Abstract

In this paper, a new two-parameter extended inverted Weibull distribution called the Inverted Weibull Poisson distribution is introduced using the Poisson generator. This method adds one shape parameter to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete
moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, stress-strength parameter, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of inverted Weibull Poisson distribution and the corresponding confidence intervals are obtained. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to the Inverted Weibull distribution.