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Counterexamples to a Central Limit Theorem and a Weak Law of Large Numbers for capacities

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  • Terán, Pedro

Abstract

Chareka (2009) presented two limit theorems in which the additivity requirement of a probability measure is weakened to a one-sided version of the inclusion–exclusion formula. Counterexamples are presented which show that both his Central Limit Theorem and his Weak Law of Large Numbers are false.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:185-189
    DOI: 10.1016/j.spl.2014.08.007
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    References listed on IDEAS

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    1. Agahi, Hamzeh & Mohammadpour, Adel & Mesiar, Radko & Ouyang, Yao, 2013. "On a strong law of large numbers for monotone measures," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1213-1218.
    2. 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.
    3. Chareka, Patrick, 2009. "The central limit theorem for capacities," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1456-1462, June.
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