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Polyache

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The statistics h_(r,s,...) defined such that

<h_(r,s,...)>=mu_rmu_s...,

where mu_r is a central moment. These statistics generalize h-statistics and were originally called "generalized h-statistics" (Tracy and Gupta 1974). The term "polyache" was introduced by Rose and Smith (2002, p. 255) by way of analogy with the polykay statistic. Polyaches are commonly defined in terms of power sums, for example

h_(2,2)=(S_1^4-2nS_1^2S_2+(n^2-3n+3)S_2^2+4(n-1)S_1S_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.

See also

h-Statistic, Polykay

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References

Rose, C. and Smith, M. D. Mathematical Statistics with Mathematica. New York: Springer-Verlag, pp. 253-256, 2002.Tracy, D. S. and Gupta, B. C. "Generalized h-Statistics and Other Symmetric Functions." Ann. Stat. 2, 837-844, 1974.

Referenced on Wolfram|Alpha

Polyache

Cite this as:

Weisstein, Eric W. "Polyache." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Polyache.html

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