Characterization of exponential distribution via regression of one record value on two non-adjacent record values

TL;DR

This paper characterizes the exponential distribution by establishing a unique regression condition involving non-adjacent record values, linking the expected median to the sample midrange given the first and last record values.

Contribution

It introduces a novel regression-based characterization of the exponential distribution using non-adjacent record values and median-midrange relationship.

Findings

Exponential distribution uniquely satisfies the regression condition.

Expected median equals sample midrange given first and last record values.

Provides a new characterization method for exponential distribution.

Abstract

We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the other next to the fixed record value, and none of them are adjacent. In particular, it turns out that the underlying distribution is exponential if and only if given the first and last record values, the expected value of the median in a sample of record values equals the sample midrange.