Precise Large Deviations for Long-Tailed Distributions |
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Authors: | Fotis Loukissas |
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Affiliation: | 1. Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83 200, Samos, Greece
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Abstract: | In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions. We prove asymptotic relations for non-random sums and for random sums of random variables with long-tailed distributions. We apply the results on two useful counting processes, namely, renewal and compound-renewal processes. |
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