### 抜粋

We study the dependence structure of bivariate order statistics from bivariate distributions, and prove that if the underlying bivariate distribution H is positive quadrant dependent (PQD) then so is each pair of bivariate order statistics. As an application, we show that if H is PQD, the bivariate distribution K^{(n)}_{+}, recently proposed by Bairamov and Bayramoglu (2012) [1], is greater than or equal to Baker's (2008) [2] distribution H^{(n)}_{+}, and hence K^{(n)}_{'} attains a correlation higher than that of H^{(n)}_{+}. We give two explicit forms of the intractable K^{(n)}_{+} and prove that for all n ≥ 2, K^{(n)}_{+} is PQD regardless of H. We also show that if H is PQD, K^{(n)}_{+} converges weakly to the Fréchet-Hoeffding upper bound as n tends to infinity.

元の言語 | English |
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ページ（範囲） | 201-208 |

ページ数 | 8 |

ジャーナル | Journal of Multivariate Analysis |

巻 | 114 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 2013 1 1 |

外部発表 | Yes |

### ASJC Scopus subject areas

- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty

## フィンガープリント Dependence structure of bivariate order statistics with applications to bayramoglu's distributions' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*Journal of Multivariate Analysis*,

*114*(1), 201-208. https://doi.org/10.1016/j.jmva.2012.07.009