The earliest and the simplest known bivariate exponential distribution, introduced by Gumbel (1960), has joint survivor function and joint probability density function given by:
S(x,y)=exp[−(αx+βy+θαβxy)] and f(x,y)=[(1−θ)αβ+θα2βx+θαβ2y+θ2α2β2xy]S(x,y) respectively, where x,y>0, α,β≥0 and 0<θ<1...