A new measure of association between random variables

作者：Asadi Majid^*

来源：Metrika, 2017, 80(6-8): 649-661.

DOI：10.1007/s00184-017-0620-5

• Association
• Correlation coefficient
• Gini's mean difference
• Mean residual life
• Cumulative residual entropy
• Frechet bounds

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 Frchet 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 . 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.

• 出版日期2017-11