On almost Sure Convergence for Negatively Superadditive Dependent Random Variables

다국어 초록 (Multilingual Abstract)

Purpose: In this paper we study the almost sure convergence for superadditive negatively dependent (NSD) random variables (r.v.’s) and obtain new results of Jamison et al. [1], Marcinkiewicz-Zygumnd type strong law, and Kolmogorov type three series theorem and some conditions in the form of NSD.
Methods: We have studied a negatively associated random variables, super additive negatively random variables, complete convergence, almost sure convergence, and Kolmogorov type three-series theorem to get the above purpose.
Results: After studying the above contents, we got the results that we wanted through the seminar. Thus, we obtained the following conclusion and this research is very important in reliability theory and probability theory and multivariate statistical analysis.
Conclusion: This paper is to study the complete convergence for weighted sums of NSD random variables and we study some preliminary results for NSD random variables and we obtained complete convergence for maximum partial sums of rowwise NSD random variables. Finally The contents of NSD has wide applications in reliability.

목차 (Table of Contents)

• 1. Introduction
• 2. Preliminaries
• 3. Main Results
• References