Only the first term of some series counts |
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| Authors: | Aurel Sp?taru |
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| Affiliation: | Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie, nr 13, 76100 Bucharest 5, Romania |
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| Abstract: | Let X,X1,X2,… be i.i.d. random variables, and set Sn=X1+?+Xn. We prove that for three important distributions of X, namely normal, exponential and geometric, series of the type ∑n≥1anP(|Sn|≥xbn) or ∑n≥1anP(Sn≥xbn) behave like their first term as x→∞. |
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| Keywords: | Tail probabilities of sums of i.i.d. random variables Normal distribution Exponential distribution Geometric distribution |
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