# Limiting behavior for arrays of row-wise upper extended negatively dependent random variables

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2 Citations (Scopus)

### Abstract

Our aim is to obtain deterministic bounds for the row sum elements of a random triangular array introducing, thereunto, a dependence structure for triangular arrays of random variables which extend the concepts of upper and lower extended negatively dependence already known for random variables. Concretely, for triangular arrays { Xn, k, 1 ≦ k≦ n, n≧ 1 } of row-wise upper extended negatively dependent random variables with dominating sequence { Mn, n≧ 1 } weakly mean dominated by a random variable X and sequences { bn} of positive constants, conditions are stated to ensure the deterministic boundedness of Σ k= 1 n(Xn, k- EXn, k) / bnLog n, where Log n: = log max { n, e}. In particular, a sufficient moment condition is given permitting us to achieve our goal under the rate of the so called “Law of the Logarithm”.

Original language English 481-492 12 Acta Mathematica Hungarica 148 2 https://doi.org/10.1007/s10474-016-0585-2 Published - 1 Apr 2016

### Fingerprint

Triangular Array
Dependent Random Variables
Limiting Behavior
Random variable
Moment Conditions
Dependence Structure
Logarithm
Boundedness
Sufficient Conditions

### Keywords

• triangular array
• upper extended negatively dependent random variable
• law of the logarithm

### Cite this

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title = "Limiting behavior for arrays of row-wise upper extended negatively dependent random variables",
abstract = "Our aim is to obtain deterministic bounds for the row sum elements of a random triangular array introducing, thereunto, a dependence structure for triangular arrays of random variables which extend the concepts of upper and lower extended negatively dependence already known for random variables. Concretely, for triangular arrays { Xn, k, 1 ≦ k≦ n, n≧ 1 } of row-wise upper extended negatively dependent random variables with dominating sequence { Mn, n≧ 1 } weakly mean dominated by a random variable X and sequences { bn} of positive constants, conditions are stated to ensure the deterministic boundedness of Σ k= 1 n(Xn, k- EXn, k) / bnLog n, where Log n: = log max { n, e}. In particular, a sufficient moment condition is given permitting us to achieve our goal under the rate of the so called “Law of the Logarithm”.",
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author = "{Lita Da Silva}, J.",
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language = "English",
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journal = "Acta Mathematica Hungarica",
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In: Acta Mathematica Hungarica, Vol. 148, No. 2, 01.04.2016, p. 481-492.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Limiting behavior for arrays of row-wise upper extended negatively dependent random variables

AU - Lita Da Silva, J.

N1 - sem pdf conforme despacho.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - Our aim is to obtain deterministic bounds for the row sum elements of a random triangular array introducing, thereunto, a dependence structure for triangular arrays of random variables which extend the concepts of upper and lower extended negatively dependence already known for random variables. Concretely, for triangular arrays { Xn, k, 1 ≦ k≦ n, n≧ 1 } of row-wise upper extended negatively dependent random variables with dominating sequence { Mn, n≧ 1 } weakly mean dominated by a random variable X and sequences { bn} of positive constants, conditions are stated to ensure the deterministic boundedness of Σ k= 1 n(Xn, k- EXn, k) / bnLog n, where Log n: = log max { n, e}. In particular, a sufficient moment condition is given permitting us to achieve our goal under the rate of the so called “Law of the Logarithm”.

AB - Our aim is to obtain deterministic bounds for the row sum elements of a random triangular array introducing, thereunto, a dependence structure for triangular arrays of random variables which extend the concepts of upper and lower extended negatively dependence already known for random variables. Concretely, for triangular arrays { Xn, k, 1 ≦ k≦ n, n≧ 1 } of row-wise upper extended negatively dependent random variables with dominating sequence { Mn, n≧ 1 } weakly mean dominated by a random variable X and sequences { bn} of positive constants, conditions are stated to ensure the deterministic boundedness of Σ k= 1 n(Xn, k- EXn, k) / bnLog n, where Log n: = log max { n, e}. In particular, a sufficient moment condition is given permitting us to achieve our goal under the rate of the so called “Law of the Logarithm”.

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KW - law of the logarithm

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DO - 10.1007/s10474-016-0585-2

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