A Multivariate Index of Dispersion

Abstract

The Fisher dispersion index is a widely used measure of dispersion in count data. In the univariate case, the dispersion index is equal to the ratio of the variance to the mean. In the multivariate case, such a widely used and applied dispersion index does not exist. In this thesis, we review some previously proposed multivariate extensions and introduce a new multivariate dispersion index. We illustrate its properties on some common multivariate discrete distributions and demonstrate its usefulness through a simulation study and real-world examples.