A k-statistic of order n is an unbiased estimator of the cumulant of order n of a population. The k-statistic of second order, for example, is the variance, the one corresponding to the third order is the skewness. Cumulants of gaussian populations are all zero from 3 on. Cumulants of Poisson populations are all constant. Cumulants help in recognizing indipendence of populations. And so on.

The purpose of the algorithm is to express k-statistics in terms of power sums: this because numerical computations made by iterating powers are more efficient either in terms of computational time either in terms of numerical errors. The alternative formula, via moments, involve symmetric functions having a more complex structure, the augumented one. 

Once you have expressed k-statistics in terms of power sums, you can replace the variables of power sums with data. 

If you select "Download attached file" in the bottom of the page you can execute the worksheet with maple program. In the maple worksheet there is the function "npolyk" that allows us to process a k-statistic or polykay replacing the simbols with numerical data.

Multisets are useful in dealing with multivariate case, since k-statistics of order n,m,etc... are computed by using multiset with n variables equal to X, m variables equal to Y and so on....