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Log-concavity of a mixture of beta distributions

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  • Mu, Xiaosheng

Abstract

We provide a sufficient condition for a mixture of Beta distributions to have log-concave density. This is true whenever the Beta distributions to be mixed together have constant parameter sum and the mixing weights are themselves log-concave. The result has applications in economics and statistics, which we present in the last section.

Suggested Citation

  • Mu, Xiaosheng, 2015. "Log-concavity of a mixture of beta distributions," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 125-130.
    • Handle: RePEc:eee:stapro:v:99:y:2015:i:c:p:125-130
    DOI: 10.1016/j.spl.2015.01.011
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    References listed on IDEAS

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    1. Geoffroy de Clippel & Kfir Eliaz & Kareen Rozen, 2014. "Competing for Consumer Inattention," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1203-1234.
    2. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    3. Chang, George T. & Walther, Guenther, 2007. "Clustering with mixtures of log-concave distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6242-6251, August.
    4. Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
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    Cited by:

    1. Ehsan Zamanzade & Xinlei Wang, 2018. "Proportion estimation in ranked set sampling in the presence of tie information," Computational Statistics, Springer, vol. 33(3), pages 1349-1366, September.

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