A Unified Approach to Construct Correlation Coefficient Between Random Variables

09/28/2018
by   Majid Asadi, et al.
0

Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the linear association between two random variables. In this paper, first we propose a covariance based unified measure of variability for a continuous random variable X and we show that several measures of variability and uncertainty, such as variance, Gini mean difference, cumulative residual entropy, etc., can be considered as special cases. Then, we propose a unified measure of correlation between two continuous random variables X and Y, with distribution functions (DFs) F and G, based on the covariance between X and H^-1G(Y) (known as the Q-transformation of H on G) where H is a continuous DF. We show that our proposed measure of association subsumes some of the existing measures of correlation. It is shown that the suggested index ranges between [-1,1], where the extremes of the range, i.e., -1 and 1, are attainable by the Frechet bivariate minimal and maximal DFs, respectively. A special case of the proposed correlation measure leads to a variant of Pearson correlation coefficient which, as a measure of strength and direction of the linear relationship between X and Y, has absolute values greater than or equal to the Pearson correlation. The results are examined numerically for some well known bivariate DFs.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/29/2019

Extreme Nonlinear Correlation for Multiple Random Variables and Stochastic Processes with Applications to Additive Models

The maximum correlation of functions of a pair of random variables is an...
research
05/09/2013

A Rank Minrelation - Majrelation Coefficient

Improving the detection of relevant variables using a new bivariate meas...
research
11/28/2017

Latent Association Mining in Binary Data

We consider the problem of identifying groups of mutually associated var...
research
02/03/2023

On the Analysis of Correlation Between Nominal Data and Numerical Data

The article investigates the possibility of measuring the strength of a ...
research
12/03/2020

Modeling Count Data via Copulas

Copula models have been widely used to model the dependence between cont...
research
06/24/2020

Estimation and Comparison of Correlation-based Measures of Concordance

We address the problem of estimating and comparing transformed rank corr...
research
07/08/2021

How to measure things

In classical information theory, a causal relationship between two rando...

Please sign up or login with your details

Forgot password? Click here to reset