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 ...

Let F be a probability distribution on R. Then there exist symmetric (about zero) random variables X and Y whose sum has distribution F if and only if F has mean zero or no mean (finite or infinite).