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Only the first term of some series counts

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  • Spataru, Aurel

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 [summation operator]n>=1anP(Sn>=xbn) or [summation operator]n>=1anP(Sn>=xbn) behave like their first term as x-->[infinity].

Suggested Citation

  • Spataru, Aurel, 2011. "Only the first term of some series counts," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1547-1551, October.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1547-1551
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    References listed on IDEAS

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    1. Pruss, Alexander R., 1997. "A two-sided estimate in the Hsu--Robbins--Erdös law of large numbers," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 173-180, October.
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