Nonnormality of Linear Combinations of Normal Random Variables |
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Authors: | G. G. Hamedani |
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Affiliation: | Department of Mathematics, Statistics, and Computer Science , Marquette University , Milwaukee , WI , 53233 , USA |
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Abstract: | Hamedani and Tata (1975) showed that the bivariate normal distribution is determined uniquely by any countably infinite collection of distinct linear combinations of the variables and by no finite number of them. It is shown here that this characterization of bivariate normal distribution cannot be extended to the multivariate case. More specifically, it is shown that the multivariate normality of subsets (r < n) of the normal variables X 1, X 2, …, Xn together with the normality of an infinite number of linear combinations of them do not guarantee the joint normality of these variables. |
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Keywords: | Characteristic function Independence Distribution function |
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