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Teoriya Veroyatnostei i ee Primeneniya, 2024, Volume 69, Issue 3, Pages 629–631
DOI: https://doi.org/10.4213/tvp5715 (Mi tvp5715) 		 
Short Communications

An example of a non-log-concave distribution where the difference has a log-concave density

M. Wang

School of Mathematics and Statistics, Wuhan University, Wuhan, China
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DOI: https://doi.org/10.4213/tvp5715
Abstract: By the Prékopa–Leindler inequality, the difference $X-X'$ has a log-concave density provided that $X$ has a log-concave density and $X$, $X'$ are independent and identically distributed. We prove that the opposite direction does not always hold true by giving an explicit example.
Keywords: log-concavity, independent difference.
Received: 01.04.2024
Published: 23.07.2024
English version:
Theory of Probability and its Applications, 2024, Volume 69, Issue 3, Pages 503–504
DOI: https://doi.org/10.1137/S0040585X97T992069
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Wang, “An example of a non-log-concave distribution where the difference has a log-concave density”, Teor. Veroyatnost. i Primenen., 69:3 (2024), 629–631; Theory Probab. Appl., 69:3 (2024), 503–504
Citation in format AMSBIB
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\by M.~Wang
\paper An example of a~non-log-concave distribution where the difference has a~log-concave density
\jour Teor. Veroyatnost. i Primenen.
\yr 2024
\vol 69
\issue 3
\pages 629--631
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\crossref{https://doi.org/10.4213/tvp5715}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4914719}
\transl
\jour Theory Probab. Appl.
\yr 2024
\vol 69
\issue 3
\pages 503--504
\crossref{https://doi.org/10.1137/S0040585X97T992069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85208912185}
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