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Standardized Moment

Defined for samples x_i, i=1, ..., N by

alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r),
(1)

where

z_i=(x_i-x^_)/(s_x).
(2)

The first few are

alpha_1=0
(3)
alpha_2=1
(4)
alpha_3=(mu_3)/(s^3)
(5)
alpha_4=(mu_4)/(s^4).
(6)

See also

Kurtosis, Moment, Skewness

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References

Kenney, J. F. and Keeping, E. S. "Moments in Standard Units." §7.8 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 98-99, 1962.

Referenced on Wolfram|Alpha

Standardized Moment

Cite this as:

Weisstein, Eric W. "Standardized Moment." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StandardizedMoment.html

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