New Formulae and Uses of Mean Absolute Deviation

Abstract

Mean absolute deviation about mean and median is extended to define “MAD-comoment” similarly analogous to classical central moment notation of covariance. Therefore, the “MAD-comoment” is used to derive the coefficient of determination in LAD regression, to analyze total sum of absolute into the pure between sum of absolute and the pure within sum of absolute that provides the exact decomposition of Pietria index of inequality, to develop a new formula for beta coefficient in financial risk analysis that gives less weight at the extreme ends than least squares method for market return and to define MAD-correlation under first moment assumption.