### 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}- E_{Xn, k}) / _{bn}Log 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 |
---|---|

Pages (from-to) | 481-492 |

Number of pages | 12 |

Journal | Acta Mathematica Hungarica |

Volume | 148 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Apr 2016 |

### Fingerprint

### Keywords

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

### Cite this

}

**Limiting behavior for arrays of row-wise upper extended negatively dependent random variables.** / Lita Da Silva, J.

Research output: Contribution to journal › Article

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”.

KW - triangular array

KW - upper extended negatively dependent random variable

KW - law of the logarithm

UR - http://www.scopus.com/inward/record.url?scp=84958772713&partnerID=8YFLogxK

U2 - 10.1007/s10474-016-0585-2

DO - 10.1007/s10474-016-0585-2

M3 - Article

VL - 148

SP - 481

EP - 492

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 2

ER -