generalized h-statistic

The statistics h_(r, s, ...) defined such that 〈h_(r, s, ...) 〉 = μ_r μ_s ..., where μ_r is a central moment. These statistics generalize h-statistics and were originally called "generalized h-statistics". The term "polyache" was introduced by Rose and Smith by way of analogy with the polykay statistic. Polyaches are commonly defined in terms of power sums, for example h_(2, 2) = (S_1^4 - 2n S_1^2 S_2 + (n^2 - 3n + 3) S_2^2 + 4(n - 1) S_1 S_3 - n(n - 1) S_4)/((n - 3)(n - 2)(n - 1) n). Polyaches can be computed using PolyH[{r, s, ...}] in the Mathematica application package mathStatica.

h-statistic | polykay