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.

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

DI NARDO, Elvira;
2009

Abstract

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.
Maple 7
Waterloo Maple Inc. 2015
http://www.maplesoft.com/applications/view.aspx?SID=33041
Estimators of cumulants and their products
E. DI NARDO; G. GUARINO; D. SENATO
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1561388
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