Only the first term of some series counts

Aurel Spataru

Statistics & Probability Letters, 2011, vol. 81, issue 10, 1547-1551

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].

Keywords: Tail; probabilities; of; sums; of; i.i.d.; random; variables; Normal; distribution; Exponential; distribution; Geometric; distribution (search for similar items in EconPapers)
Date: 2011
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