A new class of bivariate lifetime distributions

This paper introduces a new class of bivariate lifetime distributions. Let {X-i}(i 1) and {Y-i}(i 1) be two independent sequences of independent and identically distributed positive valued random variables. Define T-1 = min(X-1, ..., X-M) and T-2 = min(Y-1, ..., Y-N), where (M, N) has a discrete bivariate phase-type distribution, independent of {X-i}(i 1) and {Y-i}(i 1). The joint survival function of (T-1, T-2) is studied.