TY - JOUR
T1 - Stochastic ordering of minima and maxima from heterogeneous bivariate Birnbaum–Saunders random vectors
AU - Fang, Longxiang
AU - Zhu, Xiaojun
AU - Balakrishnan, N.
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/1/2
Y1 - 2018/1/2
N2 - In this paper, we discuss stochastic comparisons of minima and maxima arising from heterogeneous bivariate Birnbaum–Saunders (BS) random vectors with respect to the usual stochastic order based on vector majorization of parameters. Suppose the bivariate random vectors X1, X2 and X*1, X*2 follow BVBS(α1,β1,(α2,β2,ρ) and BVBS(α*1,β*1,(α*2,β*2,ρ) distributions, respectively. Suppose 0< υ≤2. We then prove that when (Formula presented.), (Formula presented.) implies (Formula presented.) and (Formula presented.) implies (Formula presented.). These results are subsequently generalized to a wider range of scale parameters. Next, we prove that when (Formula presented.), (Formula presented.) implies (Formula presented.) and (Formula presented.). Analogous results are then deduced for bivariate log BS distributions as well.
AB - In this paper, we discuss stochastic comparisons of minima and maxima arising from heterogeneous bivariate Birnbaum–Saunders (BS) random vectors with respect to the usual stochastic order based on vector majorization of parameters. Suppose the bivariate random vectors X1, X2 and X*1, X*2 follow BVBS(α1,β1,(α2,β2,ρ) and BVBS(α*1,β*1,(α*2,β*2,ρ) distributions, respectively. Suppose 0< υ≤2. We then prove that when (Formula presented.), (Formula presented.) implies (Formula presented.) and (Formula presented.) implies (Formula presented.). These results are subsequently generalized to a wider range of scale parameters. Next, we prove that when (Formula presented.), (Formula presented.) implies (Formula presented.) and (Formula presented.). Analogous results are then deduced for bivariate log BS distributions as well.
KW - Bivariate Birnbaum–Saunders distribution
KW - bivariate log Birnbaum–Saunders distribution
KW - majorization
KW - maxima
KW - minima
KW - usual stochastic order
UR - http://www.scopus.com/inward/record.url?scp=85019238100&partnerID=8YFLogxK
U2 - 10.1080/02331888.2017.1322086
DO - 10.1080/02331888.2017.1322086
M3 - Article
AN - SCOPUS:85019238100
SN - 0233-1888
VL - 52
SP - 147
EP - 155
JO - Statistics
JF - Statistics
IS - 1
ER -