# Characterization of exponential distribution through bivariate regression of record values revisited

## TL;DR

This paper revisits the characterization of the exponential distribution by examining a specific regression equation involving record values, establishing it as the unique distribution satisfying this relationship.

## Contribution

It introduces a novel regression-based characterization of the exponential distribution using bivariate record values and Beta distribution properties.

## Key findings

- Exponential distribution uniquely satisfies the regression equation.
- Regression function involves Beta distributed random variables.
- Characterization holds with a weighted average in a special case.

## Abstract

It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record values, one previous and one future, as covariates. The underlying distribution is exponential if and only if the above regression equals the expected value of an appropriately defined Beta distributed random variable. In a particular case, the expected value of the Beta variable reduces to a weighted average of the covariates.