A non-TP2 member of the asymmetric Joe extreme-value family #
Table 5 marks Joe-EV density TP2 as no* (numerical, away from independence). For
δ=1, α=β=1/2 and u=t^a, v=t^b the CDF is t^(a+b-ab/(2(a+b))). With
t=99/100, the ordered rectangles S=(0,t^180], T=(t^180,t^30], U=(t^45,t^20],
V=(t^20,1] violate the rectangle inequality implied by an MTP2 density. So this member
has no TP2 density. (The unit-weight member is Galambos, whose density-TP2 status the
paper leaves open, so the blanket claim is only checked at this member.)