In probability theory and statistics, the noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral distribution) is a noncentral generalization of the chi-squared distribution.

In probability theory and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic form of a multinormal variable (normal vector), or a linear combination of different normal variables and squares of normal variables.

The scaled inverse chi-squared distribution , where is the scale parameter, equals the univariate inverse Wishart distribution

The following are proofs of several characteristics related to the chi-squared distribution.