A Multivariate Measure of Dispersion and its Limiting Distribution

Total Variance (TV) and Generalized Variance (GV) are commonly used as a measure multivariate dispersion. However, these two statistics has some drawbacks. This paper proposes a new measure of multivariate dispersion. named Vectorial Variance (W). an inner product for set of operators defined on a Hilbert-Smith space. Since. the exact sampling distribution of V V is difficult to find. therefore the asymptotic sampling distribution is obtained.