Stochastic ordering of minima and maxima from heterogeneous bivariate Birnbaum–Saunders random vectors

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 and follow and distributions, respectively. Suppose We then prove that when , implies and implies . These results are subsequently generalized to a wider range of scale parameters. Next, we prove that when , implies and . Analogous results are then deduced for bivariate log BS distributions as well.