A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums

Gooty Divanji, Kokkada Vidyalaxmi

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DOI: 10.4236/am.2011.29163                

Abstract

Let {X_n, n ≥ 1} be a sequence of independent and identically distributed positive valued random variables with a common distribution function F. When F belongs to the domain of partial attraction of a semi stable law with index α, 0 < α < 1, an asymptotic behavior of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover’s form of law of iterated logarithm.

Keywords

Large Deviations, Law of Iterated Logarithm, Semi-Stable Law, Domain of Partial Attraction, Weighted Sums

Conflicts of Interest

The authors declare no conflicts of interest.

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