2008/07/09 by Elvira Di Nardo, E. Di Nardo, Giuseppe Guarino +2 · 2 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Probability and Statistical Research #math.CO #math.ST #msc:05A40 #msc:62H99 #msc:65C60 #msc:68W30 #stat.CO #stat.TH
paper · pdf · doi:10.1007/s11222-008-9080-0
A table with computational times, obtained with the forthcoming MathStatica release 2 (Colin Rose, private communication), has been added. In press Stat. Comp
openalex publication_date 2008/07/09 · arxiv created 2008/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.