A new class of bivariate lifetime distributions

This paper introduces a new class of bivariate lifetime distributions. Let {Xi}i ≥ 1 and {Yi}i ≥ 1 be two independent sequences of independent and identically distributed positive valued random variables. Define T1 = min (X1, …, XM) and T2 = min (Y1, …, YN), where (M, N) has a discrete bivariate phase-type distribution, independent of {Xi}i ≥ 1 and {Yi}i ≥ 1. The joint survival function of (T1, T2) is studied.