The Poisson-Paralogistic Distribution: Properties and Applications

Abstract

In this paper, a new distribution called the Poisson Paralogistic distribution (PPD) is proposed. Some properties of the new distribution which includes the density of the kth-order statistics, quantile function and value-at-risk are obtained. The maximum likelihood estimation (MLE) is then studied to obtain a parameter estimation. A simulation study shows that the MLE of the parameters of the PPD is asymptotically unbiased and consistent. The proposed distribution is applied to three real datasets and its performance is compared with some other related distributions.