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The Similarity between the Square of the Coeficient of Variation and the Gini Index

2010; Pablo de Olavide University; Issue: 10 Linguagem: Espanhol

1886-516X

Luis González Abril, Francisco Velasco Morente, José Manuel Gavilán Ruiz, Luis Sánchez-Reyes Fernández,

Business, Education, Mathematics Research

espanolEn este trabajo se obtienen diversas identidades relativas a la espezanza, varianza, covarianza, funcion de distribucion acumulada, coeficiente de variacion y curva de Lorenz que se usarian para obtener resultados teoricos interesantes. Se construye, ademas, una representacion grafica de la varianza, la cual, utilizando las propiedades obtenidas, nos indica que el cuadrado del coeficiente de variacion se puede considerar como una medida de igualdad, de igual forma que se considera al Indice de Gini. En este artIculo tambien se lleva a cabo un estudio de las similitudes entre la expresion teorica del indice de Gini y el cuadrado del coeficiente de variacion. EnglishIn this paper, several identities concerning expectation, variance, covariance, cumulative distribution functions, the coeficient 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 coeficient 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 coeficient of variation is also carried out in this paper.