A unified approach to constructing correlation coefficients between random variables

Majid Asadi () and Somayeh Zarezadeh ()
Additional contact information
Majid Asadi: University of Isfahan
Somayeh Zarezadeh: Shiraz University

Metrika: International Journal for Theoretical and Applied Statistics, 2020, vol. 83, issue 6, No 2, 657-676

Abstract: Abstract Measuring the correlation between two random variables is an important goal in various statistical applications. The standardized covariance is a widely used criterion for measuring the linear association. In this paper, first, we propose a covariance-based unified measure of variability for a continuous random variable X and show that several measures of variability and uncertainty, such as variance, Gini mean difference and cumulative residual entropy arise 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. Assuming that H is a continuous DF, the proposed measure is defined based on the covariance between X and the transformed random variable $$H^{-1}G(Y)$$H-1G(Y) (known as the Q-transformation of H on G). We show that our proposed measure of association subsumes some of the existing measures of correlation. Under some mild condition on H, it is shown that the suggested index ranges in $$[-1,1]$$[-1,1] where the extremes of the range, i.e., $$-1$$-1 and 1, are attainable by the Fréchet bivariate minimal and maximal DFs, respectively. A special case of the proposed correlation measure leads to a variant of the Pearson correlation coefficient which has absolute values greater than or equal to Pearson correlation. The results are examined numerically for some well known bivariate DFs.

Keywords: Association; Correlation coefficient; Fréchet bounds; Q-transformation; Bivariate copula (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00184-019-00759-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:83:y:2020:i:6:d:10.1007_s00184-019-00759-w

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-019-00759-w

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().