Geodesic
On the Composition of Unimodal Distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 1 (1956) no. 2, pp. 283-288

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A distribution function is called strong unimodal if its composition with any unimodal distribution function is unimodal. The following theorem is proved: For a proper unimodal distribution $F(x)$ to be strong unimodal, it is necessary and sufficient that the function $F(x)$ be continuous, and the function log $F'(x)$ be concave at a set of points where neither the right nor the left derivative of the function $F(x)$ is equal to zero. 
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     author = {I. A. Ibragimov},
     title = {On the {Composition} of {Unimodal} {Distributions}},
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     year = {1956},
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     url = {http://geodesic.mathdoc.fr/item/TVP_1956_1_2_a5/}
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I. A. Ibragimov. On the Composition of Unimodal Distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 1 (1956) no. 2, pp. 283-288. http://geodesic.mathdoc.fr/item/TVP_1956_1_2_a5/