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arXiv · 0807.5008

A new method for fast computing unbiased estimators of cumulants

E. Di Nardo·G. Guarino·D. Senato
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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.

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E. Di Nardo, G. Guarino, D. Senato. 2008-07-31. A new method for fast computing unbiased estimators of cumulants. https://doi.org/10.1007/s11222-008-9080-0

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