The maximum distribution of Kibble's bivariate gamma random vector

Bara Kim; Jeongsim Kim

doi:10.1016/j.orl.2017.06.001

The maximum distribution of Kibble's bivariate gamma random vector

Bara Kim, Jeongsim Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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{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.

Original language	English
Pages (from-to)	392-396
Number of pages	5
Journal	Operations Research Letters
Volume	45
Issue number	4
DOIs	https://doi.org/10.1016/j.orl.2017.06.001
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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10.1016/j.orl.2017.06.001

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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{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.",

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author = "Bara Kim and Jeongsim Kim",

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AU - Kim, Jeongsim

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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

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JO - Operations Research Letters

JF - Operations Research Letters

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The maximum distribution of Kibble's bivariate gamma random vector

Abstract

Keywords

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