Univariate Moments
The kth moment about the mean (or kth central moment) of a real-valued random variable X is the quantity μk := E)k], where E is the expectation operator. For a continuous univariate probability distribution with probability density function f(x) the moment about the mean μ is
For random variables that have no mean, such as the Cauchy distribution, central moments are not defined.
The first few central moments have intuitive interpretations:
- The "zeroth" central moment μ0 is one.
- The first central moment μ1 is zero (not to be confused with the first moment itself, the expected value or mean).
- The second central moment μ2 is called the variance, and is usually denoted σ2, where σ represents the standard deviation.
- The third and fourth central moments are used to define the standardized moments which are used to define skewness and kurtosis, respectively.
Read more about this topic: Central Moment
Famous quotes containing the word moments:
“Quidquid luce fuit tenebris agit: but also the other way around. What we experience in dreams, so long as we experience it frequently, is in the end just as much a part of the total economy of our soul as anything we “really” experience: because of it we are richer or poorer, are sensitive to one need more or less, and are eventually guided a little by our dream-habits in broad daylight and even in the most cheerful moments occupying our waking spirit.”
—Friedrich Nietzsche (1844–1900)