Moment (mathematics)
In mathematics, a moment is, loosely speaking, a quantitative measure of the shape of a set of points. The "second moment", for example, is widely used and measures the "width" (in a particular sense) of a set of points in one dimension or in higher dimensions measures the shape of a cloud of points as it could be fit by an ellipsoid. Other moments describe other aspects of a distribution such as how the distribution is skewed from its mean, or peaked. The mathematical concept is closely related to the concept of moment in physics, although moment in physics is often represented somewhat differently. Any distribution can be characterized by a number of features (such as the mean, the variance, the skewness, etc.), and the moments of a function describe the nature of its distribution.
The 1st moment is denoted by μ1. The first moment of the distribution of the random variable X is the expectation operator, i.e., the population mean (if the first moment exists).
In higher orders, the central moments (moments about the mean) are more interesting than the moments about zero. The first central moment is 0. The zero-th central moment, μ0 is one. The second central moment is the variance.
Other moments may also be defined. For example, the n th inverse moment about zero is and the n th logarithmic moment about zero is .
Read more about Moment (mathematics): Significance of The Moments, Cumulants, Sample Moments, Problem of Moments, Partial Moments, Central Moments in Metric Spaces
Famous quotes containing the word moment:
“That which is given to see
At any moment is the residue, shadowed
In gold or emerging into the clear bluish haze
Of uncertainty. We come back to ourselves
Through the rubbish of cloud and tree-spattered pavement.
These days stand like vapor under the trees.”
—John Ashbery (b. 1927)