Abstract:
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)F(x) to be strong unimodal, it is necessary and sufficient that the function F(x)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.
Citation:
I. A. Ibragimov, “On the Composition of Unimodal Distributions”, Teor. Veroyatnost. i Primenen., 1:2 (1956), 283–288; Theory Probab. Appl., 1:2 (1956), 255–260
\Bibitem{Ibr56}
\by I.~A.~Ibragimov
\paper On the Composition of Unimodal Distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1956
\vol 1
\issue 2
\pages 283--288
\mathnet{http://mi.mathnet.ru/tvp5002}
\transl
\jour Theory Probab. Appl.
\yr 1956
\vol 1
\issue 2
\pages 255--260
\crossref{https://doi.org/10.1137/1101021}
Linking options:
https://www.mathnet.ru/eng/tvp5002
https://www.mathnet.ru/eng/tvp/v1/i2/p283
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