On complete moment convergence for the maximal weighted sums of NSD random variables

Abstract

In this article, the complete moment convergence for weighted sums of non-identically distributed negatively superadditive dependent (NSD) random variables is investigated. Some sufficient conditions of the complete moment convergence and the complete convergence for the maximum of weighted sums of NSD random variables are established. As applications, some equivalent conditions of the complete moment convergence for a weighted version of NSD cases are presented. Our main results extend and improve the corresponding earlier ones in the literature.

Keywords:

• NSD random variables
• complete moment convergence
• equivalent conditions
• the maximal weighted sums

MATHEMATICS SUBJECT CLASSIFICATION AMS(2020)::

• 60F15

Acknowledgements

The authors are most grateful to the Editor Professor Narayanaswamy Balakrishnan and two anonymous referees for carefully reading the manuscript and for offering some valuable suggestions and comments, which greatly helped in improving an earlier version of this article.

Disclosure statement

The authors declare that they have non-financial competing interests.

Additional information

Funding

This article is supported by the Doctor and Professor Natural Science Foundation of Guilin University of Aerospace Technology (KX202103701), the Provincial Humanities and Social Science Research Project of Anhui Colleges (SK2021A0739) and the National Natural Science Foundation of China (71871046).