A MAPLE ALGORITHM FOR POLYKAYS AND MULTIVARIATE POLYKAYS

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

Received April 30, 2007

Abstract

We propose a Maple algorithm to express polykays and multivariate polykays as functions of power sums in the data points. Such algorithm is based on a symbolic computation arising from the classical umbral calculus and, so far as we know, this is the first Maple procedure for such unbiased estimators. The core of the algorithm is a routine that symbolically extends the relations between augmented monomial symmetric functions and power sums in multivariate data points. With regard to polykays, comparisons with the procedure implemented in Mathematica have shown better results in terms of computational times. For multivariate polykays no comparisons have been done, because no algorithms are known for such general estimators.

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