A new method for fast computing unbiased estimators of cumulants

  • E. Di Nardo
  • G. Guarino
  • D. SenatoEmail author


We propose new algorithms for generating k-statistics, multivariate k-statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up is obtained by means of a symbolic method arising from the classical umbral calculus. The classical umbral calculus is a light syntax that involves only elementary rules to managing sequences of numbers or polynomials. The cornerstone of the procedures here introduced is the connection between cumulants of a random variable and a suitable compound Poisson random variable. Such a connection holds also for multivariate random variables.


Univariate and multivariate k-statistics Univariate and multivariate polykays Umbral calculus 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi della BasilicataPotenzaItaly
  2. 2.Medical SchoolUniversità Cattolica del Sacro Cuore (Rome branch)RomaItaly

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