The γ-transform: A New Approach to the Study of a Discrete and Finite Random Variable

Abstract: A general method that can be used for the study of a discrete and finite random variable is presented. The method is based on the introduction of a transform of the probability density function, called γ-transform. A formula for computing the factorial moments directly from the γ-transform is derived. Moreover, it is shown how the γ-transform can be simply derived owing to its physical meaning for several combinatorial problems. Examples and applications relevant for computer science are provided