A new method for fast computing unbiased estimators of cumulants

Abstract

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.

A table with computational times, obtained with the forthcoming MathStatica release 2 (Colin Rose, private communication), has been added. In press Stat. Comp

References in corpus (2)

• A unifying framework for $k$-statistics, polykays and their multivariate generalizations
• Cumulants as non-Gaussian qualifiers

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