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تسجيل

Polykay

المؤلف:  Rose, C. and Smith, M. D.

المصدر:  Mathematical Statistics with Mathematica. New York: Springer-Verlag, 2002.

الجزء والصفحة:  ...

15-2-2021

3274

Polykay

The symmetric statistic  defined such that

(1)

where  is a cumulant. These statistics generalize k-statistic and were originally called "generalized -statistics" (Dressel 1940). The term "polykay" was introduced by Tukey (1956; Rose and Smith 2002, p. 255). Polykays are commonly defined in terms of power sums, for example

			(2)
			(3)

Polykays can be computed using PolyK[{" src="https://mathworld.wolfram.com/images/equations/Polykay/Inline10.gif" style="height:15px; width:5px" />r, s, ...}" src="https://mathworld.wolfram.com/images/equations/Polykay/Inline11.gif" style="height:15px; width:5px" />] in the Mathematica application package mathStatica.

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REFERENCES:

Cook, M. B. "Bi-Variate -Statistics and Cumulants of Their Joint Sampling Distribution." Biometrika 38, 179-195, 1951.

Dressel, P. L. "Statistical Seminvariants and Their Setimates [sic] with Particular Emphasis on Their Relation to Algebraic Invariants." Ann. Math. Stat. 11, 33-57, 1940.

Rose, C. and Smith, M. D. Mathematical Statistics with Mathematica. New York: Springer-Verlag, 2002.

Tukey, J. W. "Keeping Moment-Like Computations Simple." Ann. Math. Stat. 27, 37-54, 1956.