Characterizations of Student's t-distribution via regressions of order statistics

TL;DR

This paper characterizes a family of distributions, including the Student's t-distribution, using regression properties of order statistics, and extends these characterizations to t-distributions with higher degrees of freedom.

Contribution

It introduces new characterization results for the Student's t-distribution based on regression of order statistics, extending previous work to higher degrees of freedom.

Findings

Characterizes a family of distributions including t-distribution with 2 degrees of freedom

Extends characterization to t-distributions with more than 2 degrees of freedom

Provides a new approach to understanding distribution properties via order statistics

Abstract

Utilizing regression properties of order statistics, we characterize a family of distributions introduced by Akhundov, Balakrishnan, and Nevzorov (2004), that includes the t-distribution with two degrees of freedom as one of its members. Then we extend this characterization result to t-distribution with more than two degrees of freedom.