In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. \cite{Wang 8}, but also partially improve the corresponding ones of Huang et al. \cite{Huang 16}.
In this work, a complete moment convergence theorem is obtained for weighted sums of asymptotically almost negatively associated (AANA) random variables without assumption of identical distribution under some mild moment conditions. As an application, the complete convergence theorems for weighted sums of negatively associated (NA) and AANA random variables are obtained. The result not only generalizes the corresponding ones of Sung \cite{15} and Huang et al. \cite{16}, but also improves them.
We prove the complete convergence of Shannon's, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.
The authors first establish the Marcinkiewicz-Zygmund inequalities with exponent p (1≤p≤2) for m-pairwise negatively quadrant dependent (m-PNQD) random variables. By means of the inequalities, the authors obtain some limit theorems for arrays of rowwise m-PNQD random variables, which extend and improve the corresponding results in [Y. Meng and Z. Lin (2009)] and [H. S. Sung (2013)]. It is worthy to point out that the open problem of [H. S. Sung, S. Lisawadi, and A. Volodin (2008)] can be solved easily by using the obtained inequality in this paper.