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A new measure of association between random variables

Author

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  • Majid Asadi

    (University of Isfahan
    Institute of Research in Fundamental Sciences (IPM))

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.

Suggested Citation

  • Majid Asadi, 2017. "A new measure of association between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 649-661, November.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0620-5
    DOI: 10.1007/s00184-017-0620-5
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    References listed on IDEAS

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    1. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
    2. Cuadras, C. M., 2002. "On the Covariance between Functions," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 19-27, April.
    3. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
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    Cited by:

    1. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    2. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2019. "Cumulative Measure of Inaccuracy and Mutual Information in k -th Lower Record Values," Mathematics, MDPI, vol. 7(2), pages 1-19, February.

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