### 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 |

### Fingerprint

### 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

### Cite this

*Operations Research Letters*,

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

**The maximum distribution of Kibble's bivariate gamma random vector.** / Kim, Bara; Kim, Jeongsim.

Research output: Contribution to journal › Article

*Operations Research Letters*, vol. 45, no. 4, pp. 392-396. https://doi.org/10.1016/j.orl.2017.06.001

}

TY - JOUR

T1 - The maximum distribution of Kibble's bivariate gamma random vector

AU - Kim, Bara

AU - Kim, Jeongsim

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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{Y1,Y2} when a random vector (Y1,Y2) follows Kibble's BGD with integral shape parameter. This is achieved by showing that max{Y1,Y2} has the same distribution as the first passage time of a continuous time Markov process.

AB - 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{Y1,Y2} when a random vector (Y1,Y2) follows Kibble's BGD with integral shape parameter. This is achieved by showing that max{Y1,Y2} has the same distribution as the first passage time of a continuous time Markov process.

KW - Downton's bivariate exponential distribution

KW - First passage time

KW - Kibble's bivariate gamma distribution

UR - http://www.scopus.com/inward/record.url?scp=85021653421&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021653421&partnerID=8YFLogxK

U2 - 10.1016/j.orl.2017.06.001

DO - 10.1016/j.orl.2017.06.001

M3 - Article

AN - SCOPUS:85021653421

VL - 45

SP - 392

EP - 396

JO - Operations Research Letters

JF - Operations Research Letters

SN - 0167-6377

IS - 4

ER -