*

The

*
th
*
-statistic
*
is the distinctive symmetric unbiased estimator the the cumulant
*
that a offered statistical distribution, i.e.,
*
is identified so that


*

where

*
(Kenney and Keeping 1951, p.189; Rose and also Smith 2002, p.256). In addition, the variance


*

is a minimum contrasted to all various other unbiased estimators (Halmos 1946; Rose and also Smith 2002, p.256). Most authors (e.g., Kenney and also Keeping 1951, 1962) usage the notation

*
because that
*
-statistics, while Rose and Smith (2002) choose
*
.

You are watching: What does k mean in statistics

The

*
-statistics have the right to be provided in terms of the sums the the
*
th strength of the data point out as


*

then

*
*
*

*
*
*

(Fisher 1928; Rose and also Smith 2002, p.256). These deserve to be provided by KStatistic in the Mathematica applications package mathStatica.

For a sample size

*
, the first few
*
-statistics are given by

*
*
*

where

*
is the sample mean,
*
is the sample variance, and
*
is the
*
th sample central moment (Kenney and also Keeping 1951, pp.109-110, 163-165, and 189; Kenney and Keeping 1962).

The variances the the first few

*
-statistics are provided by

*
*
*

(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
REFERENCES:

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.


Referenced top top surfacetoairnewyork.com|Alpha: k-Statistic
CITE THIS AS:

Weisstein, Eric W. "k-Statistic." Fromsurfacetoairnewyork.com--A surfacetoairnewyork.com net Resource. Https://surfacetoairnewyork.com/k-Statistic.html


surfacetoairnewyork.com net Resources
Mathematica»

The #1 tool for producing Demonstrations and anything technical.

surfacetoairnewyork.com|Alpha»

Explore anything with the an initial computational knowledge engine.

surfacetoairnewyork.com Demonstrations Project»

Explore thousands of cost-free applications throughout science, mathematics, engineering, technology, business, art, finance, social sciences, and also more.

Computerbasedmath.org»

Join the initiative for modernizing mathematics education.

Online Integral Calculator»

Solve integrals v surfacetoairnewyork.com|Alpha.

Step-by-step Solutions»

Walk through homework difficulties step-by-step from start to end. Hints aid you try the following step on her own.

surfacetoairnewyork.com trouble Generator»

Unlimited random exercise problems and answers with integrated Step-by-step solutions. Exercise online or make a printable study sheet.

surfacetoairnewyork.com education Portal»

Collection the teaching and also learning tools constructed by surfacetoairnewyork.com education experts: dynamic textbook, great plans, widgets, interaction Demonstrations, and also more.

See more: 4730 Crystal Springs Dr Los Angeles Ca 90027, 4730 Crystal Springs Dr, Los Angeles, Ca 90027

surfacetoairnewyork.com Language»

Knowledge-based programming because that everyone.


*
contact the surfacetoairnewyork.com Team
© 1999-2021 surfacetoairnewyork.com Research, Inc. | regards to Use