### 抄録

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 |
---|---|

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 |

外部発表 | Yes |

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### ASJC Scopus subject areas

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

### これを引用

*Journal of Multivariate Analysis*,

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

**Dependence structure of bivariate order statistics with applications to bayramoglu's distributions.** / Huang, J. S.; Dou, Xiaoling; Kuriki, Satoshi; Lin, G. D.

研究成果: Article

*Journal of Multivariate Analysis*, 巻. 114, 番号 1, pp. 201-208. https://doi.org/10.1016/j.jmva.2012.07.009

}

TY - JOUR

T1 - Dependence structure of bivariate order statistics with applications to bayramoglu's distributions

AU - Huang, J. S.

AU - Dou, Xiaoling

AU - Kuriki, Satoshi

AU - Lin, G. D.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Baker's bivariate distribution

KW - Fréchet-hoeffding bounds

KW - Hoeffding's representation for covariance

KW - Negative quadrant dependent

KW - Pearson's correlation

KW - Positive quadrant dependent

UR - http://www.scopus.com/inward/record.url?scp=84867740607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867740607&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2012.07.009

DO - 10.1016/j.jmva.2012.07.009

M3 - Article

AN - SCOPUS:84867740607

VL - 114

SP - 201

EP - 208

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 1

ER -