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

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DOI: 10.4236/am.2011.29163    3,183 Downloads   5,837 Views   Citations

ABSTRACT

Let {Xn, 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

G. Divanji and K. Vidyalaxmi, "A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums," Applied Mathematics, Vol. 2 No. 9, 2011, pp. 1175-1181. doi: 10.4236/am.2011.29163.

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