Characterizations of probability distributions via bivariate regression of record values

TL;DR

This paper extends existing characterizations of exponential distributions using bivariate regression of record values to include non-adjacent covariates and monotone transformations, covering means like weighted, geometric, and harmonic.

Contribution

It introduces new characterizations of probability distributions by analyzing regression of record values with non-adjacent covariates and transformations.

Findings

Extended characterization to non-adjacent record values

Included transformations involving means such as weighted, geometric, harmonic

Provided new regression-based distribution characterizations

Abstract

Bairamov et al. (Aust N Z J Stat 47:543-547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.