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Article: The Complications of the Fourth Central Moment.
- Article from:
- The American Statistician
- Article date:
- August 1, 1999
- Author:
CopyrightCOPYRIGHT 1999 American Statistical Association. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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This article illustrates the additional complications in the mathematical formulas involving the fourth central moment in comparison with those involving the first moment, the second central moment, and the third central moment.
KEY WORDS: Central moments; Cumulants; Descriptive statistics; Moments; Unbiased estimation.
1. INTRODUCTION
In an introductory statistics course, moments and central moments of a random variable are interpreted descriptively. The first moment (the mean) and the second central moment (the variance) are introduced to describe, respectively, the location and the dispersion of a random variable. Then the third and the ...