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The central limit theorem for capacities

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  • Chareka, Patrick

Abstract

In investigations where the parameter of interest is the mean or expectation of some random variable and the underlying probability measure (distribution) is unknown, one usually appeals to the central limit theorem, provided it holds. In this article the central limit theorem and the weak law of large numbers for capacities are presented. Capacities are non-additive probability measures which provide alternative and plausible measures of likelihood or uncertainty when the assumption of additivity is suspect. Some examples of practical problems in game theory, economics and finance that can be solved at least partially, by the central limit theorem for capacities, are presented.

Suggested Citation

  • Chareka, Patrick, 2009. "The central limit theorem for capacities," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1456-1462, June.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:12:p:1456-1462
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    References listed on IDEAS

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    1. Marinacci, Massimo, 1999. "Limit Laws for Non-additive Probabilities and Their Frequentist Interpretation," Journal of Economic Theory, Elsevier, vol. 84(2), pages 145-195, February.
    2. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
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    Cited by:

    1. Terán, Pedro, 2015. "Counterexamples to a Central Limit Theorem and a Weak Law of Large Numbers for capacities," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 185-189.

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