Post date: Feb 23, 2014 8:26:21 PM
Sébastien suggested that the Fréchet case was less interesting than the wiggled independent case, i.e., with correlations near zero. I don't really know how to use Cholesky decomposition to get precisely specified (Pearson) correlations among beta deviates, but I tried it anyway, and got these correlations
[a] [b] [c] [d] [e]
[a] 1.00000000 0.1267407 0.09715921 0.1273015 0.09917538
[b] 0.12674066 1.0000000 0.11033749 0.1289528 0.10258259
[c] 0.09715921 0.1103375 1.00000000 0.1134578 0.10834225
[d] 0.12730153 0.1289528 0.11345779 1.0000000 0.11899527
[e] 0.09917538 0.1025826 0.10834225 0.1189953 1.00000000
With this wiggled state of dependence, we got these results
which seem to be indistinguishable from the independent results. I suspect the deviations from independence could get pretty large and the results would stay pretty much the same (so long as were always using a normal copula and these rather big reliabilities).
Scott