### 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 |
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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 |

### Keywords

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