# Moment ## 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. ### Definitions 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. ### References *