Shape Measures based on Mean Absolute Deviation with Graphical Display

Abstract

Mean absolute deviation about median is partitioned into two parts in terms of median to obtain a measure of skewness that is zero for symmetric distributions and into four parts in terms of percentiles to obtain a measure of equality between the middle and the sides of a distribution that is zero for the normal distribution. Based on these partitions a powerful and informative graph called H-graph is produced that can provide more insight into the nature of the data and assess goodness of fit for a data set to a theoretical model. This graph enriches the visual information offered by the histogram and box-plot. By using these measures two tests for middle-sides equality and normality are proposed. The simulation results from several distributions show that the proposed tests have a very good power in comparisons with well-known powerful tests that depend on moments.