Development of a Simple Bivariate Correlation Model for Nonlinearly-Related Asymmetrically-Distributed Variables

Abstract

With a view to measuring the joint effects of nonlinearity and asymmetry on bivariate associations, this study presented Pearson correlation as an equivalent simple regression model for two standard Gaussian random variables. Based on this equivalence relationship, correlation model was formulated under some mixture of skew-normality and nonlinearity assumptions. Subsequently, the adequacy of proposed model was evaluated in a comprehensive simulation study. Estimated correlation values from the proposed technique were compared with those from some three commonly-used techniques of Pearson, Spearman and Kendall. Empirical findings showed that in all mixtures of levels of skewness and degrees of nonlinearity, the proposed gave correct values of: For varying levels of skewness and nonlinearity, the three other methods gave correct correlation coefficients only for Kendall’s, in particular, did not give correct values for any degrees of nonlinearity and levels of skewness.