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Strictly log-concave probability distributions in discrete response models

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  • Eleni Aristodemou

Abstract

This paper extends the results of Prekopa (1973, 1980) on strictly log-concave cumulative distributions to strictly log-concave probability distributions. It is shown that if a random variable follows a strictly logarithmic concave distribution, then the probability that the random variable is contained within a convex polytope is also strictly logarithmic concave. This formal result can be useful for identification and estimation of a general class of linear-index discrete response models, where the additively separable unobservable follows a strictly log-concave distribution.

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  • Eleni Aristodemou, 2022. "Strictly log-concave probability distributions in discrete response models," University of Cyprus Working Papers in Economics 06-2022, University of Cyprus Department of Economics.
    • Handle: RePEc:ucy:cypeua:06-2022
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    References listed on IDEAS

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    2. Greene,William H. & Hensher,David A., 2010. "Modeling Ordered Choices," Cambridge Books, Cambridge University Press, number 9780521142373, September.
    3. Delle Site, Paolo & Kilani, Karim & Gatta, Valerio & Marcucci, Edoardo & de Palma, André, 2019. "Estimation of consistent Logit and Probit models using best, worst and best–worst choices," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 87-106.
    4. Greene,William H. & Hensher,David A., 2010. "Modeling Ordered Choices," Cambridge Books, Cambridge University Press, number 9780521194204, September.
    5. Simon Peters & Andrew Chesher, 2000. "On the Use of Enumeration for Investigating the Performance of Hypothesis Tests for Economic Models with a Discrete Response Variable," Computational Economics, Springer;Society for Computational Economics, vol. 15(3), pages 273-289, June.
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    Keywords

    Discrete Response Models; Strict Log-Concavity;

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