Polykay
المؤلف:
Rose, C. and Smith, M. D.
المصدر:
Mathematical Statistics with Mathematica. New York: Springer-Verlag, 2002.
الجزء والصفحة:
...
15-2-2021
2827
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
Polykays can be computed using PolyK[![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/Polykay/Inline10.gif" style="height:15px; width:5px" />r, s, ...![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/Polykay/Inline11.gif" style="height:15px; width:5px" />] in the Mathematica application package mathStatica.
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.
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