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Moment (mathematics)
Measure of the shape of a function
Moment (mathematics)
In mathematics, moments of a function are certain quantitative measures related to the shape of the function's graph. For example, in physics, if the function represents mass density, then the zeroth moment is the total mass, the first moment is the center of mass (multiplied by total mass), and the second moment is the moment of inertia. In statistics, 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. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from 0 to ∞) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem).
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