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<p>Probability distributions on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{R}\)</EquationSource> </InlineEquation> which are strongly unimodal according to I.A. Ibragimov are studied in the paper. It is proposed the correct proof that the property of logarithmic concavity of the distribution density is sufficient property for its stgrong unimodality when its support coincides with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb{R}\)</EquationSource> </InlineEquation>.</p>

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Absolutely continuous, logarithmically concave unimodal distributions

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Yuri P. Virchenko,
  • Amanuel M. Tewolde

摘要

Probability distributions on \(\mathbb{R}\) which are strongly unimodal according to I.A. Ibragimov are studied in the paper. It is proposed the correct proof that the property of logarithmic concavity of the distribution density is sufficient property for its stgrong unimodality when its support coincides with \(\mathbb{R}\) .