arXiv subjects

Tran Loc Hung

Publications and source records attributed to Tran Loc Hung.

2 recordsLinked to original sources

arXiv2023

On the Rotar central limit theorem for sums of a random number of independent random variables

The Rotar central limit theorem is a remarkable theorem in the non-classical version since it does not use the condition of asymptotic infinitesimality for the independent individual summands, unlike the theorems named Lindeberg's and Lindeberg-Feller's in the classical version. The Rotar central limit theorem generalizes the classical Lindeberg-Feller central limit theorem since the Rotar condition is weaker than Lindeberg's. The main aim of this paper is to introduce the Rotar central limit theorem for sums of a random number of independent (not necessarily identically distributed) random variables and the conditions for its validity. The order of approximation in this theorem is also considered in this paper.

math.PR↗

arXiv2023

Classical and non-classical central limit theorems for random sums of independent random variables of a double sequence

Since the appearance of H. Robbins article (1948), the central limit theorems for random sums have been studied for about 70 years. The central limit theorems for random sums of independent random variables play a very important role in various disciplines such as statistics, financial mathematics, insurance, etc. The purpose of this paper is to randomize some well-known classical and non-classical central limit theorems for sums of independent (not necessarily identically distributed) random variables of a double sequence, with the conditions for determining their validity. The results obtained in this paper are extensions and generalizations of known ones.

math.PR↗