Moment

From Glossary of Meteorology
Revision as of 18:32, 26 January 2012 by imported>Perlwikibot (Created page with " {{TermHeader}} {{TermSearch}} <div class="termentry"> <div class="term"> == moment == </div> #<div class="definition"><div class="short_definition">The product of a di...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)



moment

  1. 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.

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

    The symbol μn′ (or νn) is used for a raw moment as distinguished from the corresponding central moment μn taken about the mean μ. Thus the raw moments are
    ams2001glos-Me24
    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
    ams2001glos-Me25
    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.