Upper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded ...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or, more specifically, subexponential random variables. A key application of this ...

In the present paper a uniform asymptotic series is derived for the probability distribution of the sum of a large number of independent random variables. In contrast to the usual Edgeworth-type ...