Q and Umbral Calculus and Statistical Methods

Dattoli Pino, ENEA Frascati Labs Fusion Department

In this talk we discuss the theory of non-standard calculus applied to the study of non-standard statistical distributions. New methods of calculus have provided means extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to infer those of the aforementioned distributions. We develop a point of view aimed at merging umbral and q-calculus and show that this new technique is tailor suited to get further progress in the mathematical handling of the Tsallis distributions.

Area: CS1 - Algebraic methods in Statistics and Probability (Elvira Di Nardo)

Keywords: umbral calculus, q-calculus

Please Login in order to download this file