structural:reformatting, information:filtering, information:extraction
Homoscedastic distributions

Two or more normal distributions, N (μ 1, Σ 1), N (μ 2, Σ 2), {\displaystyle N(\mu _{1},\Sigma _{1}),N(\mu _{2},\Sigma _{2}),} are both homoscedastic and lack serial correlation if they share the same diagonals in their covariance matrix, Σ 1 i i = Σ 2 j j, ∀ i = j. {\displaystyle \Sigma _{1}{ii}=\Sigma _{2}{jj},\ \forall i=j.} and their non-diagonal entries are zero. Homoscedastic distributions are especially useful to derive statistical pattern recognition and machine learning algorithms. One popular example of an algorithm that assumes homoscedasticity is Fisher's linear discriminant analysis.The concept of homoscedasticity can be applied to distributions on spheres.