Overview
Statistical moments are the expectation (integral with respect to probability measure) of various powers of a random variable.
That is, the {% n^{th} %} moment of the random variable {% X %} is
{% \mathbb{E}(X^n) %}
For most applications, the relevant quantity is the centered moments, that is
{% \mathbb{E}[(X-\mu)^n] %}
The centered moments are given specific names, such as variance (see below). Typically when referring to the {% n^{th} %}
moment of a variable, the author means the uncentered moment.
Centered Moments
The following represent the first four moments of a distribution.
Topics
- Moments and Linear Algebra - when the random variables in question are vectors, the moments have simple expressions using matrix algebra.
- Probability Hilbert Space - recasting a probability space as a Hilbert Space using the moments.
Tools
The following tools are available for calculating statistic moments from a dataset.