Geodesic
Reversion of Chebyshev's inequality
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 873-878

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Without using complex analysis, we deduce a lower estimate for the distribution tail of a random variable in terms of its moment-generating function.
Keywords: moment-generating function, Young–Fenchel transformation. 
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     author = {D. R. Bagdasarov and E. I. Ostrovskii},
     title = {Reversion of {Chebyshev's} inequality},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {873--878},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a11/}
}
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D. R. Bagdasarov; E. I. Ostrovskii. Reversion of Chebyshev's inequality. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 4, pp. 873-878. http://geodesic.mathdoc.fr/item/TVP_1995_40_4_a11/