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In this paper, we shall establish a new almost sure convergence of negatively associated sequence under the assumption $$\mathbb {E}( |X|^p\log ^{-\alpha } |X|)$$ E ( | X | p log - α | X | ) for some $$\alpha \ge 0$$ α ≥ 0 and $$p\in (0,2)$$ p ∈ ( 0 , 2 ) , from which the classic Marcinkiewicz–Zygmund strong law of large numbers is deduced. We further point out...
Let {Xn, n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the Lp-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.
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