Moment

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 × ρu, 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.
By analogy, in statistical terminology, the mean value of a power of a random variable.

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 are
where E(xⁿ) is the expected value of the variate x to the nth power. In particular, μ₀′ ≡ 1 and μ₁′ ≡ ν₁ ≡ μ. The central moments are
where E[(x − μ)ⁿ] is the expected value of the nth power of the deviation of the variate from its mean. In particular, μ₀ ≡ 1, μ₁ ≡ 0, μ₂ ≡ σ², where σ² is the variance.