# Estimators of the correlation coefficient in the bivariate exponential distribution

## TL;DR

This paper derives a lower bound on the estimation error of the correlation coefficient in bivariate exponential distributions and evaluates the efficiency of three nonlinear estimators, highlighting their performance across different correlation ranges.

## Contribution

It introduces a finite-support parameter constraint to establish a lower bound and compares the optimality of three nonlinear estimators for the correlation coefficient.

## Key findings

- The cosine similarity-based estimator is highly efficient for correlation > 0.35.
- The transformed Pearson correlation performs better for smaller correlation values.
- A lower bound on estimation error is derived under the finite-support constraint.

## Abstract

A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of three estimators, each being a nonlinear function of moments of exponential or Rayleigh observables. The estimator based on a measure of cosine similarity is shown to be highly efficient for values of the correlation coefficient greater than 0.35; for smaller values, however, it is the transformed Pearson correlation coefficient that exhibits errors closer to the derived bound.