A new measure of association between random variables

Majid Asadi ()
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Majid Asadi: University of Isfahan

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 6, No 3, 649-661

Abstract: 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 , 1]. We show that the extremes of the range, i.e., $$-1$$ - 1 and 1, are attainable by the Fr $$\acute{\mathrm{e}}$$ 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 $$\rho $$ ρ . 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.

Keywords: Association; Correlation coefficient; Gini’s mean difference; Mean residual life; Cumulative residual entropy; Fr $$\acute{\mathrm{e}}$$ e ´ chet bounds (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00184-017-0620-5

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