Sentence examples for arrays of dependent from inspiring English sources

We also establish a Hájek-Rényi-type maximal inequality for multidimensional arrays of random elements and some maximal moment inequalities for arrays of dependent random elements.

Mean convergence theorems for weighted sums of an array of dependent random variables satisfying this condition of integrability are obtained.

In this paper, we obtain weak laws of large numbers for the array of dependent random variables satisfying the condition of residually ( r, h ) -integrable with respect to the array of constants { a n i }.

The first statistical approach tested the hypothesis that there were significant gender x diagnosis interactions across the array of dependent variables (DVs), viewing each of the DVs in isolation.

Recently, complete convergence for arrays of rowwise dependent random variables has been considered.

A vast array of culture dependent analytical methods and protocols for food safety testing has been developed during the past decades.

Let { X n i, i ≥ 1, n ≥ 1 } be an array of negatively dependent random variables which are stochastically dominated by a random variable X.

In this paper, we obtain complete convergence results for weighted sums of arrays of rowwise negatively dependent random variables.

Then ∑ n = 1 ∞ b n P ( | ∑ i = 1 ∞ X n i | > ϵ ) < ∞ for all ϵ > 0. In this section, we obtain two complete convergence results for weighted sums of arrays of rowwise negatively dependent random variables.

Since a n i ≥ 0, { a n i X n i ′, i ≥ 1, n ≥ 1 } and { a n i X n i ″, i ≥ 1, n ≥ 1 } are also arrays of rowwise negatively dependent random variables.

Bacteria display an array of contact-dependent interaction systems that have evolved to facilitate direct cell-to-cell communication.