A property of coefficients of variation for ordered bivariate log-normal variables
Donald D. Lien, David Rearden · Communication in Statistics- Theory and Methods · 1996
This paper considers the maximum and minimum of a pair of log-normal variables with equal mean. It shows that either order statistic has a smaller coefficient of variation than the two original log-normal variables provided the latter are of equal variance. When the variances are unequal, as the variance ratio increases, the minimum (maximum), has a smaller coefficient of variation if the correlation coefficient of the log-normal variables is small (small) and the variances are large (small).