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Sample Raw Moment


The rth sample raw moment m_r^' of a sample with sample size n is defined as

 m_r^'=1/nsum_(k=1)^nx_k^r.
(1)

The sample raw moments are unbiased estimators of the population raw moments,

 <m_r^'>=mu_r^'.
(2)

(Rose and Smith 2002, p. 253). The sample raw moment m_r^' is related to power sums S_r by

 m_r^'=(S_r)/n.
(3)

This relationship can be given by SampleRawToPowerSum[r] in the Mathematica application package mathStatica.


See also

Central Moment, Raw Moment, Sample, Sample Central Moment, Sample Mean

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References

Rose, C. and Smith, M. D. Mathematical Statistics with Mathematica. New York: Springer-Verlag, p. 253, 2002.

Referenced on Wolfram|Alpha

Sample Raw Moment

Cite this as:

Weisstein, Eric W. "Sample Raw Moment." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SampleRawMoment.html

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