Abstract: The present paper consider risk of the restricted maximum likelihood estimators (RMLE) of order means of two sample distribution exponential, λ₁≤λ₂, with the same sample size, under symmetric entropy loss. It proved that RMLE λ_i have smaller risk than usual sample means X_i(i=1,2). The asymptotic efficiencies e(λ_i,X_i) of RMLE λ_i with respect to sample means X_i for λ₂/λ₁→∞ and n→∞ have also been discussed.

Key words: order restriction, symmetric entropy loss, efficiency, restricted maximun likelihood estimator