Characterizations of exponential distribution via conditional expectations of record values

TL;DR

This paper characterizes the exponential distribution by proving it uniquely satisfies a regression identity involving the conditional expectation of the sample mean of record values given two external record values.

Contribution

It introduces a novel characterization of the exponential distribution through a specific regression identity involving record values.

Findings

Exponential distribution uniquely satisfies the regression identity.

Conditional expectation of sample mean relates to record values in exponential distribution.

Provides a new characterization method for exponential distribution.

Abstract

We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.