### Abstract

Bivariate gamma distribution (BGD) can be used in hydrology, stochastic modeling and reliability theory. We derive the Laplace–Stieltjes transform of the distribution of max{Y_{1},Y_{2}} when a random vector (Y_{1},Y_{2}) follows Kibble's BGD with integral shape parameter. This is achieved by showing that max{Y_{1},Y_{2}} has the same distribution as the first passage time of a continuous time Markov process.

Original language | English |
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Pages (from-to) | 392-396 |

Number of pages | 5 |

Journal | Operations Research Letters |

Volume | 45 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 Jul 1 |

### Keywords

- Downton's bivariate exponential distribution
- First passage time
- Kibble's bivariate gamma distribution

### ASJC Scopus subject areas

- Software
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics

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## Cite this

Kim, B., & Kim, J. (2017). The maximum distribution of Kibble's bivariate gamma random vector.

*Operations Research Letters*,*45*(4), 392-396. https://doi.org/10.1016/j.orl.2017.06.001