TY - JOUR
T1 - The maximum distribution of Kibble's bivariate gamma random vector
AU - Kim, Bara
AU - Kim, Jeongsim
N1 - 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.
PY - 2017/7
Y1 - 2017/7
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
UR - http://www.scopus.com/inward/record.url?scp=85021653421&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2017.06.001
DO - 10.1016/j.orl.2017.06.001
M3 - Article
AN - SCOPUS:85021653421
VL - 45
SP - 392
EP - 396
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 4
ER -