The asymptotic distribution of a truncated sample mean for the extremely heavy-tailed distributions

Fuquan Tang and Dong Han

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 14, 5168-5185

Abstract: This article deals with the asymptotic distribution for the extremely heavy-tailed distributions with infinite mean or variance by using a truncated sample mean. We obtain three necessary and sufficient conditions under which the asymptotic distribution of the truncated test statistics converges to normal, neither normal nor stable or converges to −∞ or the combination of stable distributions, respectively. The numerical simulation illustrates an application of the theoretical results above in the hypothesis testing.

Date: 2024
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DOI: 10.1080/03610926.2023.2209231

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