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Robustness of the sample correlation - the bivariate lognormal case

The sample correlation coefficient R is almost universally used to estimate the population correlation coefficient ρ. If the pair (X,Y) has a bivariate normal distribution, this would not cause any trouble. However, if the marginals are nonnormal, particularly if they have high skewness and kurtosis, the estimated value from a sample may be quite different from the population correlation coefficient ρ.