In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, a polykay, or generalised k-statistic, (denoted
) is a statistic defined as a
linear combination of
sample moment
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total ma ...
s.
Etymology
The word ''polykay'' was coined by
American
American(s) may refer to:
* American, something of, from, or related to the United States of America, commonly known as the "United States" or "America"
** Americans, citizens and nationals of the United States of America
** American ancestry, pe ...
mathematician
John Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...
in 1956, from ''poly'', "many" or "much", and ''kay'', the phonetic spelling of the letter "k", as in
k-statistic
In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant
In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the '' moments'' of the ...
.
[Tukey, J. W. (1956.) "Keeping Moment-Like Computations Simple", ''Ann. Math. Stat.'', 27:37–54.]
References
{{Statistics-stub
Symmetric functions
Statistical inference