Generalized variance i.e. the determinant of the covariance matrix is a scalar measure of multivariate distribution dispersion. The exact distribution of the generalized variance is known only for multivariate normal vectors. For random vectors in high dimensional spaces it has a complicated formula very troublesome to apply. An estimator of the logarithm of generalized variance derived with the help of limit theorems for random determinants was presented as well as its properties in examples of chosen simulation multivariate distributions.
generalized variance, random vector, covariance matrix, random determinant
 Anderson T.W., , An introduction to multivariate statistical analysis, John Wiley and Sons, NY, London.
 Barra J.R., , Matematyczne podstawy statystyki, PWN, Warszawa.
 Girko V.L., , Random Matrices (in Russian), Kiev University, Kiev.
 Girko V.L., , Spectral Theory of Random Matrices (in Russian), Nauka, Moscow.
 Girko V.L., , Statistical Analysis of Observations of Increasing Dimension, Kluwer Academic Publishers.
 Girko V.L., , Theory of Random Determinants, Kluwer Academic Publisher.
 Johnson B.A., Abramovich Y.I., Mestre X., [Aug. 2008], MUSIC, G-MUSIC,and Maximum- Likelihood Performance Breakdown, IEEE Transactions on Signal Processing, Vol. 56, No. 2.
 Krzyśko M., , Wielowymiarowa analiza statystyczna, Rektor UAM, Poznań.
 Rao C.R., , Modele liniowe statystyki matematycznej, PWN, Warszawa.