ABSTRACT
In multivariate statistical analysis multivariate normal distribution plays a very dominant role. Many results relating to univariate normal statistical inference have been successfully extended to the multivariate normal distribution. In practice, the verification of the assumption that a given set of data arises from a multivariate normal population is cumbersome. A natural question thus arises how sensitive these results are to the assumption of multinormality. In recent years one such investigation involves in considering a family of density functions having many similar properties as the multinormal. The family of elliptically symmetric distributions contains probability density functions whose contours of equal probability have elliptical shapes. In recent years this family is becoming increasingly popular because of its frequent use in “filtering and stochastic control” (Chu (1973)), “random signal input” (McGraw and Wagner (1968)), “stock market data analysis” (Zellner (1976)) and because some optimum results of statistical inference in the multivariate normal preserves their properties for all members of the family. The family of “spherically symmetric distributions” is a special case of this family.
