A New Poisson Inverted Exponential Distribution: Model, Properties and Application

Abstract

A new Poisson Inverted Exponential distribution is developed from the Poisson family of distribution, which has two parameters. The characteristic of the intended model is unimodal, positive skewed and platykurtic, while the characteristic of the hazard function is the inverted bathtub and the decreasing order. Explicit expression of quantile function, moments (including incomplete and conditional moments), moment generating function, residual life function, R`enyi and q-entropies, probability weighted moment and order statistics of the intended model. The value of unknown parameters is estimated by the maximum likelihood estimate with the confidence interval. Similarly, purposed model compared with well-known other five distributions through different criteria like as goodness of fit, P-P plot, Q-Q plots and K-S test. Likewise, we fitted the PDF and CDF of purposed model with other models, it is clear that intended model is great flexibility and satisfactory fit than those models. Therefore purposed model is more useful in real data and life time data analysis and modelling.