## Abstract

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.

Original language | English |
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Pages (from-to) | 201-208 |

Number of pages | 8 |

Journal | Journal of Multivariate Analysis |

Volume | 114 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 |

Externally published | Yes |

## Keywords

- Baker's bivariate distribution
- Fréchet-hoeffding bounds
- Hoeffding's representation for covariance
- Negative quadrant dependent
- Pearson's correlation
- Positive quadrant dependent

## ASJC Scopus subject areas

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