Abstract
In the light of an inequality derived by Chernoff (1981), a characterization of the normal distribution was obtained by Borovkov and Utev (1983). Prakasa Rao and Sreehari (1986) derived a multivariate analogue characterizing the multivariate normal distribution. A bound is obtained for the variation between the probability distribution of a random vector with mean zero and a finite covariance matrix Σ and the corresponding multivariate normal distribution with mean zero and the same covariance matrix Σ. As applications, characterization of a multivariate normal distribution due to Prakasa Rao and Sreehari (1986) is derived and a multivariate limit theorem is given. Results obtained extend the work of Utev (1989). Inter alia, an integro-differential inequality valid for random vectors with finite covariance matrix is obtained.
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