Geodesic
An analogue of Сhernoff–Вorovkov–Utev inequality and related characterization
Teoriâ veroâtnostej i ee primeneniâ, Tome 36 (1991) no. 3, pp. 609-612
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Chernoff–Borovkov–Utev inequality, which bounds the variances of functions of normal random variables, also characterizes normality. We present an inequality for the mean deviations of functions of random variables and demonstrate that it characterizes Laplace's double exponential distribution. 
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     title = {An analogue of {{\CYRS}hernoff{\textendash}{\CYRV}orovkov{\textendash}Utev} inequality and related characterization},
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M. Freimer; G. S. Mudholkar. An analogue of Сhernoff–Вorovkov–Utev inequality and related characterization. Teoriâ veroâtnostej i ee primeneniâ, Tome 36 (1991) no. 3, pp. 609-612. http://geodesic.mathdoc.fr/item/TVP_1991_36_3_a24/