Limit theorems for sums of random variables with mixture distribution

TL;DR

This paper investigates the asymptotic behavior of sums of mixed distribution random variables, revealing how the interplay of mixing and truncation influences their limiting distributions.

Contribution

It provides a comprehensive analysis of the limit theorems for sums of random variables with mixture distributions, considering the dependence of parameters on the number of summands.

Findings

Characterization of limiting distributions under different parameter regimes

Impact of mixing coefficient and truncation level on fluctuations

Extension of classical limit theorems to mixture distributions

Abstract

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions of the sums due to various relations between these parameters.