The similarity between the square of the coefficient of variation and the Gini index of a general random variable

In this paper, several identities concerning expectation, variance, covariance, cumulative distribution functions, the coefficient of variation, and the Lorenz curve are obtained and they are used in establishing theoretical results. Furthermore, a graphical representation of the variance is proposed which, together with the aforementioned identities, enables the square of the coeffcient of variation to be considered as an equality measure in the same way as is the Gini index. A study of the similarities between the theoretical expression of the Gini index and the square of the coefficient of variation is also carried out in this paper.