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Exponential probability inequalities for WNOD random variables and their applications

Research paper by Aiting Shen, Mei Yao, Wenjuan Wang, Andrei Volodin

Indexed on: 23 Jun '15Published on: 23 Jun '15Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas



Abstract

Some exponential probability inequalities for widely negative orthant dependent (WNOD, in short) random variables are established, which can be treated as very important roles to prove the strong law of large numbers among others in probability theory and mathematical statistics. By using the exponential probability inequalities, we study the complete convergence for arrays of rowwise WNOD random variables. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. In addition, the complete moment convergence for arrays of rowwise WNOD random variables is studied by using the exponential probability inequality and complete convergence that we established.