On the convergence rate for arrays of row-wise NOD random variables

Abstract

In this article, the complete convergence results of weighted sums for arrays of rowwise negatively orthant dependent (NOD) random variables are investigated. Some sufficient conditions for complete convergence for arrays of rowwise NOD random variables are presented without assumption of identical distribution.

Keywords:

• Negatively orthant dependent random variables
• Arrays of rowwise random variables
• Complete convergence.

Mathematics Subject Classification:

• 60F15.

Acknowledgments

The authors are deeply grateful to Editor-in-Chief Prof. N. Balakrishnan and anonymous referees whose insightful comments and suggestions contributed substantially to the improvement of this article.

Funding

Supported by the National Natural Science Foundation of China (11201001, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1508085J06), the Provincial Natural Science Research Project of Anhui Colleges (KJ2015A018), the Research Teaching Model Curriculum of Anhui University (xjyjkc1407), the Quality Improvement Projects for Undergraduate Education of Anhui University (ZLTS2015035) and the Students Innovative Training Project of Anhui University (201510357118).