Fast algorithms for k-statistics, polykays and their multivariate generalization

This algorithm has been inserted in the MapleSoft Application Center. We provide four algorithms to generate single and multivariate k-statistics and single and multivariate polykays. The computational times are very fast compared with the procedures available in the literature. Such speeding up is obtained through a symbolic method arising from the classical umbral calculus. The classical umbral calculus is a light syntax to manage sequences of numbers or polynomials, involving only elementary rules. The keystone of the procedures here introduced is the connection, achieved by a symbolic device, between cumulants of a random variable and a suitable compound Poisson random variable. Such a connection holds also for multivariate random variables.