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On the max-domain of attraction of distributions with log-concave densities

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  • Müller, Samuel
  • Rufibach, Kaspar

Abstract

We show that both parametric distribution functions appearing in extreme value theory have log-concave densities if the extreme value index [gamma][set membership, variant][-1,0] and that all distribution functions F with log-concave density belong to the max-domain of attraction of the generalized extreme value distribution with [gamma][set membership, variant][-1,0].

Suggested Citation

  • Müller, Samuel & Rufibach, Kaspar, 2008. "On the max-domain of attraction of distributions with log-concave densities," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1440-1444, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1440-1444
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    References listed on IDEAS

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    1. Mark Yuying An, 1996. "Log-concave Probability Distributions: Theory and Statistical Testing," Game Theory and Information 9611002, University Library of Munich, Germany.
    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. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
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    Cited by:

    1. Samuel Müller & Houng Chhay, 2011. "Partially smooth tail-index estimation for small samples," Computational Statistics, Springer, vol. 26(3), pages 491-505, September.
    2. Alfredo Di Tillio & Marco Ottaviani & Peter Norman Sørensen, 2021. "Strategic Sample Selection," Econometrica, Econometric Society, vol. 89(2), pages 911-953, March.

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