Abstract
A characterization of the normal distribution by a statistical independence on a linear transformation of two mutually independent random variables is proved by using the convolution inequality for the Fisher information.
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Itoh, Y. An application of the convolution inequality for the Fisher information. Ann Inst Stat Math 41, 9–12 (1989). https://doi.org/10.1007/BF00049105
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DOI: https://doi.org/10.1007/BF00049105