High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the specific name generalized chi-squared distribution (also generalized chi-square distribution) arises in relation to one particular family of variants of the chi-squared distribution. There are several other such variants for which the same term is sometimes used, or which clearly are generalizations of the chi-squared distribution, and which are treated elsewhere: some are special cases of the family discussed here, for example the noncentral chi-squared distribution and the gamma distribution, while the generalized gamma distribution is outside this family. The type of generalisation of the chi-squared distribution that is discussed here is of importance because it arises in the context of the distribution of statistical estimates in cases where the usual statistical theory does not hold. For example, if a predictive model is fitted by least squares but the model errors have either autocorrelation or heteroscedasticity, then a statistical analysis of alternative model structures can be undertaken by relating changes in the sum of squares to an asymptotically valid generalized chi-squared distribution. More specifically, the distribution can be defined in terms of a quadratic form derived from a multivariate normal distribution.