Opposition-Based Computing H.R. Tizhoosh, M. Ventresca, S. Rahnamayan . . . . . . . . . . . . . . . . . . . . . . . . . 11 Antithetic and Negatively Associated Random Variables and Function Maximization Don L. McLeish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Opposition and Circularity F. G. Asenjo . . . . . . . . . . . . . . . . . ...

An exponential inequality is established for identically distributed negatively associated random variables which have the finite Laplace transforms. The inequality improves the results of Kim and Kim 2007 , Nooghabi and Azarnoosh 2009 , and Xing et al. 2009 . We also obtain the convergence rate O 1 n1/2 logn −1/2 for the strong law of large numbers, which improves the corresponding ones of Kim...

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process gen...

We investigate the complete convergence of partial sums of randomly weighted extended negatively dependent (END) random variables. Some results of complete moment convergence, complete convergence and the strong law of large numbers for this dependent structure are obtained. As an application, we study the convergence of the state observers of linear-time-invariant systems. Our results extend t...

We give lower bounds on the joint entropy of n pairwise independent random variables. We show that if the variables have no dominant value (their min-entropies are bounded away from zero) then this joint entropy grows as Ω(log n). This rate of growth is known to be best possible. If k-wise independence is assumed, we obtain an optimal Ω(k log n) lower bound for not too large k. We also show tha...

In a sequence of random variables, record values are observations that exceed or fall below the current extreme value.Now consider a sequence of pairwise random variables  {(Xi,Yi), i>=1}, when the experimenter is interested in studying just thesequence of records of the first component, the second component associated with a record value of the first one is termed the concomitant of that ...

In a celebrated work by Shao [13] several inequalities for negatively associated random variables were proved. In this paper we obtain some maximal inequalities for associated random variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].