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Suppose the random variablesfollow normal distributions,, and their dependence is modelled by Archimedean copula with generator  ϕ . Then, the following results are established for the largest order statistics: (1) Supposeandare increasing in  t &gt;0, then, ifandforwe have; (2) Supposeis decreasing andis increasing in  t &gt;0, then, ifandforwe have; (3) Supposeandare increasing in  t &gt;0, then, ifandforwe have; (4) Supposeis decreasing andis increasing in  t &gt;0, then, ifandforwe have. Analogous results are then established for smallest order statistics as well. In addition, we present some numerical examples to illustrate all the results established here. Finally, some concluding remarks are made.

Orderings of extremes from dependent Gaussian variables with Archimedean copula under simple tree order restrictions