Polykay
Alternate name
Definition
The symmetric statistic k_(r, s, ...) defined such that 〈k_(r, s, ...) 〉 = κ_r κ_s ..., where κ_r is a cumulant. These statistics generalize k-statistic and were originally called "generalized k-statistics". The term "polykay" was introduced by Tukey. Polykays are commonly defined in terms of power sums, for example k_(1, 1) | = | (S_1^2 - S_2)/((n - 1) n) k_(1, 2) | = | (-S_1^3 + (n + 1) S_1 S_2 - n S_3)/((n - 2)(n - 1) n). Polykays can be computed using PolyK[{r, s, ...}] in the Mathematica application package mathStatica.
Related terms
