Abstract
We propose a new measure of association between two continuous random variables X and Y based on the covariance between X and the log-odds rate associated to Y. The proposed index of correlation lies in the range [\(-1\), 1]. We show that the extremes of the range, i.e., \(-1\) and 1, are attainable by the Fr\(\acute{\mathrm{e}}\)chet bivariate minimal and maximal distributions, respectively. It is also shown that if X and Y have bivariate normal distribution, the resulting measure of correlation equals the Pearson correlation coefficient \(\rho \). Some interpretations and relationships to other variability measures are presented. Among others, it is shown that for non-negative random variables the proposed association measure can be represented in terms of the mean residual and mean inactivity functions. Some illustrative examples are also provided.
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Acknowledgements
The author would like to thank an anonymous reviewer for comments and suggestions which improved the exposition of the article. This research work was carried out in IPM Isfahan branch and was in part supported by a Grant from IPM (No. 95620411).
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Asadi, M. A new measure of association between random variables. Metrika 80, 649–661 (2017). https://doi.org/10.1007/s00184-017-0620-5
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DOI: https://doi.org/10.1007/s00184-017-0620-5