On uses of mean absolute deviation: decomposition, skewness and correlation coefficients

The mean absolute deviation about mean is expressed as a covariance between a random variable and its under/over indicator functions. Based on this representation new correlation coefficients are derived. These correlation coefficients ensure high stability of statistical inference when we deal with distributions that are not symmetric and for which the normal distribution is not an appropriate approximation. The covariance representation of the mean absolute deviation allows obtaining a semi decomposition of Pietra’s index for income from different resources. Moreover, a measure of skewness based on the mean absolute deviation is discussed. By using simulation study it is shown that the mean absolute deviation correlation is outperforming the Pearson’s correlation for non-normal model. Copyright Sapienza Università di Roma 2012