Polyache
المؤلف:
Rose, C. and Smith, M. D
المصدر:
Mathematical Statistics with Mathematica. New York: Springer-Verlag
الجزء والصفحة:
...
15-2-2021
1445
Polyache
The statistics 
defined such that
where 
is a central moment. These statistics generalize h-statistics and were originally called "generalized 
-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
Polyaches can be computed using PolyH[![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/Polyache/Inline4.gif" style="height:15px; width:5px" />r, s, ...![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/Polyache/Inline5.gif" style="height:15px; width:5px" />] in the Mathematica application package mathStatica.
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 
-Statistics and Other Symmetric Functions." Ann. Stat. 2, 837-844, 1974.
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