# Moments

From Glossary of Meteorology

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## moment

- The product of a distance and another parameter.

The moment may be about a point, line, or plane; if the parameter is a vector, the moment is the vector product of the vector distance from the point, line, or plane, into the parameter. Thus, the moment of the momentum of a fluid parcel per unit volume about an axis is**r**× ρ**u**, where**r**is the vector from axis to the parcel, ρ the density, and**u**the velocity vector of the parcel; this is also called the angular momentum. The moment of a force**F**about an axis is**r**×**F**, called the torque. The second moment of a parameter is the moment of the first moment, and so on, for higher moments.

The symbol μ_{n}′ (or ν_{n}) is used for a raw moment as distinguished from the corresponding central moment μ_{n}taken about the mean μ. Thus the raw moments arewhere*E*(*x*^{n}) is the expected value of the variate*x*to the*n*th power. In particular, μ_{0}′ ≡ 1 and μ_{1}′ ≡ ν_{1}≡ μ. The central moments arewhere*E*[(*x*- μ)^{n}] is the expected value of the*n*th power of the deviation of the variate from its mean. In particular, μ_{0}≡ 1, μ_{1}≡ 0, μ_{2}≡ σ^{2}, where σ^{2}is the variance.

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