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

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

3 Citations (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

Bibliographical note

Funding Information:
We are grateful to the area editor for valuable comments and suggestions, which improved this paper. B. Kim's research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2014R1A2A2A01005831). J. Kim's research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A4A01003813).

Publisher Copyright:
© 2017 Elsevier B.V.

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

Cite this

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title = "The maximum distribution of Kibble's bivariate gamma random vector",

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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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.

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The maximum distribution of Kibble's bivariate gamma random vector

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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