An example of a non-log-concave distribution where the difference has a log-concave density
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911343052849152 |
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| author | Wang, Min |
| author_facet | Wang, Min |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An example of a non-log-concave distribution where the difference has a log-concave density Wang, Min Probability 60E05 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. |
| title | An example of a non-log-concave distribution where the difference has a log-concave density |
| topic | Probability 60E05 |
| url | https://arxiv.org/abs/2512.23179 |