Univariate Moments
The kth moment about the mean (or kth central moment) of a real-valued random variable X is the quantity μk := E)k], where E is the expectation operator. For a continuous univariate probability distribution with probability density function f(x) the moment about the mean μ is
For random variables that have no mean, such as the Cauchy distribution, central moments are not defined.
The first few central moments have intuitive interpretations:
- The "zeroth" central moment μ0 is one.
- The first central moment μ1 is zero (not to be confused with the first moment itself, the expected value or mean).
- The second central moment μ2 is called the variance, and is usually denoted σ2, where σ represents the standard deviation.
- The third and fourth central moments are used to define the standardized moments which are used to define skewness and kurtosis, respectively.
Read more about this topic: Central Moment
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