Mean Difference and Mean Deviation of Tukey Lambda Distribution

The purpose of this paper is to broaden the knowledge of mean difference and, in particular, of an important distribution model known as Tukey lambda, which is generally used to choose a model to fit data. We have obtained compact formulas, which are not yet reported in literature, of mean deviation and mean difference related to the said distribution model. These results made it possible to analyze the relationships among variability indexes, namely standard deviation, mean deviation and mean difference, regarding Tukey lambda model.