Characterizations of the Logistic and Related Distributions

TL;DR

This paper reviews recent advances in characterizing the logistic distribution, introduces new results using order statistics and exponential shifts, and explores related Pareto type II distribution properties.

Contribution

It provides new characterization results for the logistic distribution and investigates related Pareto type II distribution using distributional equalities.

Findings

New characterization results for the logistic distribution.

Characterization of Pareto type II distribution.

Use of order statistics and exponential shifts in characterizations.

Abstract

It is known that few characterization results of the logistic distribution were available before, although it is similar in shape to the normal one whose characteristic properties have been well investigated. Fortunately, in the last decade, several authors have made great progress in this topic. Some interesting characterization results of the logistic distribution have been developed recently. In this paper, we further provide some new results by the distributional equalities in terms of order statistics of the underlying distribution and the random exponential shifts. The characterization of the closely related Pareto type II distribution is also investigated.