释义 |
MomentThe th moment of a distribution about zero is defined by
 | (1) |
where
 | (2) |
, the Mean, is usually simply denoted . If the moment is instead taken about a point ,
 | (3) |
The moments are most commonly taken about the Mean. These moments are denoted and are defined by
 | (4) |
with . The moments about zero and about the Mean are related by
The second moment about the Mean is equal to the Variance
 | (8) |
where is called the Standard Deviation.
The related Characteristic Function is defined by
 | (9) |
The moments may be simply computed using the Moment-Generating Function,
 | (10) |
A Distribution is not uniquely specified by its moments, although it is by its Characteristic Function.See also Characteristic Function, Charlier's Check, Cumulant-Generating Function, Factorial Moment,Kurtosis, Mean, Moment-Generating Function, Skewness, Standard Deviation, StandardizedMoment, Variance References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Moments of a Distribution: Mean, Variance, Skewness, and So Forth.'' §14.1 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 604-609, 1992.
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