Generalization of the partial summation process (Q2714736)

The aim of the paper is to study two transformation types of discrete random variables and some of their relationships. The first transformation considered is a generalization of the partial summation derived from a process met in the theoretical explorations of the Bradford law, but represents also a mathematical model of law-like hypotheses in linguistics and musicology. The second transformation is defined as a summation depending on the probability mass function of the discrete random variable. The relations between probability generating functions and moments of the parent and descendant distributions are analyzed. The author shows that the Salvia-Bollinger distribution is invariant with respect to the considered transformations of discrete random variables.