Characterizations of Two-Points and Other Related Distributions

TL;DR

This paper introduces new characterizations of two-point and related distributions using properties of independence and linear forms, expanding understanding of their distributional properties.

Contribution

It provides novel characterizations of two-point and related distributions based on independence and linear forms, enriching the theoretical framework.

Findings

New characterization of two-point distributions

Characterizations involving independence and linear forms

Insights into related distributions like uniform and squared hyperbolic secant

Abstract

We provide new characterizations of two-points and some related distributions. We use properties of independence and/or identity of the distributions of suitable linear forms of random variables. Keywords: characterization of a distribution; two-points distribution; uniform distribution; squared hyperbolic secant distribution; independent or identically distributed linear forms