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The laws of large numbers for Pareto-type random variables with infinite means

Author

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  • Wenzhi Yang
  • Lei Yang
  • Da Wei
  • Shuhe Hu

Abstract

In this paper, we consider the laws of large numbers for NSD random variables satisfying Pareto-type distributions with infinite means. Based on the Pareto-Zipf distributions, some weak laws of large numbers for weighted sums of NSD random variables are obtained. Meanwhile, we show that a weak law for Pareto-Zipf distributions cannot be extended to a strong law. Furthermore, based on the two tailed Pareto distribution, a strong law of large numbers for weighed NSD random variables is presented. Our results extend the corresponding earlier ones.

Suggested Citation

  • Wenzhi Yang & Lei Yang & Da Wei & Shuhe Hu, 2019. "The laws of large numbers for Pareto-type random variables with infinite means," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(12), pages 3044-3054, June.
  • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:12:p:3044-3054
    DOI: 10.1080/03610926.2018.1473602
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    Cited by:

    1. Bernou, Ismahen & Boukhari, Fakhreddine, 2022. "Limit theorems for dependent random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Rita Giuliano & Milto Hadjikyriakou, 2021. "On Exact Laws of Large Numbers for Oppenheim Expansions with Infinite Mean," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1579-1606, September.

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