A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application

Abstract

This paper proposes a new heavy-tailed and alternative slash type distribution on a bounded interval via a relation of a slash random variable with respect to the standard logistic function to model the real data set with skewed and high kurtosis which includes the outlier observation. Some basic statistical properties of the newly defined distribution are studied. We derive the maximum likelihood, least-square, and weighted least-square estimations of its parameters. We assess the performance of the estimators of these estimation methods by the simulation study. Moreover, an application to real data demonstrates that the proposed distribution can provide a better fit than well-known bounded distributions in the literature when the skewed data set with high kurtosis contains the outlier observations.