The laws of large numbers for Pareto-type random variables with infinite means |
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| Authors: | Wenzhi Yang Lei Yang Da Wei |
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| Institution: | 1. School of Mathematical Sciences, Anhui University, Hefei, PR China;2. School of Mathematical and Physical Sciences, Nanyang Technological University, Singapore |
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| 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. |
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| Keywords: | Law of large numbers infinite mean pareto type distribution |
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