Sample Raw Moment

The th sample raw moment  of a sample with sample size  is defined as

(1)

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

(2)

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

(3)

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

REFERENCES:

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