Moment in Statistics

  • In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.

  • If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis.

  • The mathematical concept is closely related to the concept of moment in physics.


Suppose that we have a random variable X and the moments considered below have convergence (< +inf.), then

  • E[X^k] is the k-th order moment to the origin,

  • E[(X-E[X])^k] is the k-th order central moment,

  • E[(X-E[X])^k]/sigma^k is the k-th order standardized moment, which is the k-th order central moment normalized by sigma^k.


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