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Modulation of symmetry for discrete variables and some extensions

Substantial work has been dedicated in recent years to the construction of families of continuous distributions obtained by applying a modulation factor to a base symmetric density so as to obtain non‐symmetric variant forms, often denoted skew‐symmetric distributions. All this development has dealt with the case of continuous variables, while here we extend the formulation to the discrete case; moreover, some of the statements are of general validity. The results are illustrated with an application to the distribution of the score difference in sport matches. Copyright © 2014 John Wiley & Sons, Ltd