The maximum distribution of Kibble's bivariate gamma random vector

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)392-396
Number of pages5
JournalOperations Research Letters
Volume45
Issue number4
DOIs
Publication statusPublished - 2017 Jul 1

Fingerprint

Reliability theory
Bivariate Distribution
Hydrology
Gamma distribution
Random Vector
Markov processes
Continuous-time Markov Process
Reliability Theory
Stochastic Modeling
First Passage Time
Shape Parameter
Transform
Markov process
Continuous time
Integral
First passage time
Stochastic modeling

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

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

In: Operations Research Letters, Vol. 45, No. 4, 01.07.2017, p. 392-396.

Research output: Contribution to journalArticle

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