(Kenney and Keeping 1951, p.189). In the special case of a typical parent population, an unbiased estimator because that is provided by
(Kenney and Keeping 1951, pp.189-190).
For a limited population, allow a sample size be taken native a populace size . Climate unbiased estimators for the populace mean , for the population variance , for the population skewness , and because that the population kurtosis overabundance are
(Church 1926, p.357; Carver 1930; Irwin and Kendall 1944; Kenney and also Keeping 1951, p.143), whereby is the sample skewness and also is the sample kurtosis excess.
SEE ALSO: Cumulant, h-Statistic, Kurtosis, Mean, Moment, common Distribution, Polykay, Sample main Moment, Skewness, Statistic, Unbiased Estimator, Variance
Carver, H.C. (Ed.). "Fundamentals that the theory of Sampling." Ann.Math. Stat. 1, 101-121, 1930.
Church, A.E.R. "On the method and Squared Standard-Deviations ofSmall Samples from any Population." Biometrika 18, 321-394, 1926.
Fisher, R.A. "Moments and Product moment of Sampling Distributions."Proc. London Math. Soc. 30, 199-238, 1928.
Halmos, P.R. "The theory of Unbiased Estimation." Ann. Math. Stat. 17,34-43, 1946.
Irwin, J.O. And also Kendall, M.G. "Sampling moments of Moments for aFinite Population." Ann. Eugenik 12, 138-142, 1944.
Kenney, J.F. And also Keeping, E.S. Mathematicsof Statistics, Pt.2, 2nd ed. Princeton, NJ: valve Nostrand, 1951.
Kenney, J.F. And Keeping, E.S. "The -Statistics." §7.9 in mathematics of Statistics, Pt.1, 3rd ed. Princeton, NJ: valve Nostrand, pp.99-100, 1962.
Rose, C. And Smith, M.D. "k-Statistics: Unbiased Estimators that Cumulants." §7.2C in mathematics Statistics v Mathematica. Brand-new York: Springer-Verlag, pp.256-259, 2002.
Stuart, A.; and Ord, J.K. Kendall"s advanced Theory the Statistics, Vol.2A: classical Inference & the straight Model, sixth ed. New York: Oxford university Press, 1999.
Ziaud-Din, M. "Expression of the k-Statistics and also in terms of Power Sums and also Sample Moments." Ann. Math. Stat. 25, 800-803, 1954.
Ziaud-Din, M. "The Expression that -Statistic in regards to Power Sums and Sample Moments." Ann. Math. Stat. 30, 825-828, 1959.
Ziaud-Din, M. And also Ahmad, M. "On the Expression that the -Statistic in regards to Power Sums and also Sample Moments." Bull. Internat. Stat. Inst. 38, 635-640, 1960.
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