ON LARGE DEVIATION PROBABILITIES FOR PROPERLYNORMALIZED WEIGHTED SUMS AND RELATED LAW OF ITERATED LOGARITHM
Keywords:Large deviation probability, weighted sum, law of iterated logarithm
Let be a sequence of independent and identically distributed random variables withdistribution function F. When F belongs to the domain of attraction of a stable law with index α, 0 <α < 2 and α≠1, an asymptotic behaviour 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.
Allan Gut (1986): Law of iterated logarithm
for subsequences, Probab. Math-Statist. 7(1),
Beuerman, D.R (1975): Limit distributions
for sums of weighted random variables,
Chover, J (1966): A law of iterated
logarithm for stable summands, Proc. Amer.
Drasin, D and Seneta, E (1986): A
generalization of slowly varying functions.
Gooty Divanji (2004): Law of iterated
logarithm for subsequences of partial sums
which are in thedomain of partial attraction
of semi stable law, Probability and
Mathematical Statistics, Vol.24, Fasc. 2,41,
Heyde.C.C (1967a): A contribution to the
theory of large deviations for sums of
independentrandom variables, Zeitschrift.
fur Wahr. Und ver. Geb, band 7, 303-308.
Heyde.C.C (1967b): On large deviation
problems for sums of random variables
which are notattracted to the normal law,
Ann. Math. Statist. 38(5), 1575-1578.
Heyde.C.C (1968): On large deviation
probabilities in the case of attraction to a
non normal stable law,Sankhya, ser. A, 30,
Ingrid Torrang (1987): Law of iterated
logarithm - Cluster points of deterministic
and random subsequences, Prob.Math.
Statist. 8, 133-141.
Liang Peng and Yongcheng Qi (2003):
Chover-type laws of the iterated logarithm
for weightedsums, Statistics and
Probability letters, 65, 401-410.
Rainer Schwabe and Allan Gut (1996): On
the law of the iterated logarithm for rapidly
increasingsubsequences. Math.Nachr. 178,
Vasudeva, R (1984): Chover's law of
iterated logarithm and weak convergence,
ActaMath.Hungar. 44(3-4), 215-221.
Vasudeva, R and Divanji, G (1991): Law
of iterated logarithm for random
subsequences, Statistics and Probability
letters 12, 189-194.
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