## Abstract

In this paper, we discuss stochastic comparisons of minima and maxima arising from heterogeneous bivariate Birnbaum–Saunders (BS) random vectors with respect to the usual stochastic order based on vector majorization of parameters. Suppose the bivariate random vectors X_{1}, X_{2} and X^{*}_{1}, X^{*}_{2} follow BVBS(α_{1},β_{1},(α_{2},β_{2},ρ) and BVBS(α^{*}_{1},β^{*}_{1},(α^{*}_{2},β^{*}_{2},ρ) distributions, respectively. Suppose 0< υ≤2. We then prove that when (Formula presented.), (Formula presented.) implies (Formula presented.) and (Formula presented.) implies (Formula presented.). These results are subsequently generalized to a wider range of scale parameters. Next, we prove that when (Formula presented.), (Formula presented.) implies (Formula presented.) and (Formula presented.). Analogous results are then deduced for bivariate log BS distributions as well.

Original language | English |
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Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | Statistics |

Volume | 52 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2 Jan 2018 |

Externally published | Yes |

## Keywords

- Bivariate Birnbaum–Saunders distribution
- bivariate log Birnbaum–Saunders distribution
- majorization
- maxima
- minima
- usual stochastic order