On large deviation probabilities for sums of random variables which are attracted to the normal law

1 January 1973

journal article
research article
Published by Taylor & Francis in Communications in Statistics

Vol. 2 (6) , 525-533
https://doi.org/10.1080/03610927308827095

Abstract

For the sequence {x_n of independent identically distributed random variable satisrying P{x₁>x} x L(x) and P{-x₁>x} x L₁(x),where p≥2 and L,L₁ are functions of slow variation such that L₁(x)/L(x)−p as x→∞,it is shown that P{S_n>>t_a}∽np{X₁>>t_n}for certain sequences t_n;here

Keywords

This publication has 4 references indexed in Scilit:

Large deviation probabilities for positive random variables
Proceedings of the American Mathematical Society, 1970
On Large Deviation Problems for Sums of Random Variables which are not Attracted to the Normal Law
The Annals of Mathematical Statistics, 1967
A contribution to the theory of large deviations for sums of independent random variables
Probability Theory and Related Fields, 1967
A pair of complementary theorems on convergence rates in the law of large numbers
Mathematical Proceedings of the Cambridge Philosophical Society, 1967