The maximum distribution of Kibble's bivariate gamma random vector

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)392-396
Number of pages5
JournalOperations Research Letters
Volume45
Issue number4
DOIs
Publication statusPublished - 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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