Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

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 this article, the complete convergence for weighted sums of widely orthant dependent (WOD, in short) random variables without identical distribution is investigated. In addition, the complete ...

Let $W_{n}\coloneq \sum_{j=1}^{n}Z_{j}$ be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability ...