Mathematics – Statistics Theory
Scientific paper
2008-07-31
Mathematics
Statistics Theory
A table with computational times, obtained with the forthcoming MathStatica release 2 (Colin Rose, private communication), has
Scientific paper
10.1007/s11222-008-9080-0
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.
Guarino Giuseppe
Nardo Elvira Di
Senato Domenico
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