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

Wenzhi Yang, Lei Yang, Da Wei and Shuhe Hu

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 12, 3044-3054

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.

Date: 2019
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DOI: 10.1080/03610926.2018.1473602

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