A MAPLE ALGORITHM FOR POLYKAYS AND MULTIVARIATE POLYKAYS

E. Di Nardo (Italy), G. Guarino (Italy) and D. Senato (Italy)

Received April 30, 2007

References:

[1] D. F. Andrews and J. E. Stafford, Symbolic computation for statistical inference, Oxford Statistical Science Series, 21, Oxford University Press, Oxford, 2000. [2] E. Di Nardo, G. Guarino and D. Senato, A unifying framework for k-statistics, polykays and their multivariate generalizations, Preprint: arXiv:math.CO/0607623v1. [3] E. Di Nardo and D. Senato, Umbral nature of the Poisson random variables, Algebraic Combinatorics and Computer Science, eds., H. Crapo and D. Senato, Springer-Verlag, Italia, 2001, pp. 245-266. [4] E. Di Nardo and D. Senato, A symbolic method fork-statistics, Appl. Math. Lett. 19 (2006), 968-975. [5] E. Di Nardo and D. Senato, An umbral setting for cumulants and factorial moments, Eur. J. Combinatorics 27 (2006), 394-413. [6] P. Dressel, Statistical seminvariants and their estimates with particular emphasis on their relation to algebraic invariants, Ann. Math. Statist. 11 (1940), 33-57. [7] R. A. Fisher, Moments and product moments of sampling distributions, Proc. London Math. Soc. Part (2), 30 (1929), 199-238. [8] S. M. Roman and G. C. Rota, The umbral calculus, Adv. Math. 27 (1978), 95-188. [9] C. Rose and M. D. Smith, Mathematical Statistics with Mathematica, Springer- Verlag, New York, 2002. [10] G. C. Rota and B. D. Taylor, The classical umbral calculus, SIAM J. Math. Anal. 25 (1994), 694-711. [11] J. R. Stembridge, A maple package for symmetric functions, J. Symbolic Comput. 20 (1995), 755-768. [12] A. Stuart and J. Ord, Kendall’s Advanced Theory of Statistics, Vol. 1, Charles Griffin and Company Limited, London, 1987. [13] J. Tukey, Some sampling simplified, J. Amer. Statist. Assoc. 45 (1950), 501-519.

Keywords and phrases: cumulants, k-statistics, polykays, umbral calculus, symmetric polynomials.