Abstract: For scaleparameter family c(x,n)η^-νe^-T(x)/η, we dealt with the property of the Bayes estimator and the admissible estimator of η=τ^r with the theory of intergral transformation, under the function of symmetricentropy loss L(η,d)=ν(η/d+d/η-2), for a random sample of size n arising from scaleparameter population {(1/τ) f(x/τ), τ>0}. We have proved the invariance of the two estimators in one-one mapping.

Key words: symmetric entropy loss, Bayes estimator, admissible estimator, scale parameter, invariance