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

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

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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

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

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10.1016/j.orl.2017.06.001