Mixed Estimators of Ordered Scale Parameters of Two Gamma Distributions withArbitrary Known Shape Parameters

When an ordering among parameters is known in advance,the problem of estimating the smallest or the largest parametersarises in various practical problems. Suppose independent randomsamples of size ni drawn from two gamma distributions withknown arbitrary shape parameter ni 0 and unknown scale parameterβi 0, i = 1, 2. We consider the class of mixed estimators ofβ1 and β2 under the restriction 0 β1 (less-than or equivalent) β2. It has been shownthat a subclass of mixed estimators of i, beats the usual estimatorsXi/vi, i = 1, 2, and a class of admissible estimators in the classof mixed estimators are derived under scale-invariant squared errorloss function. Also it has been shown that the mixed estimator of(β1, β2), 0 β1 (less-than or equivalent) β2, beats the usual estimator (X1/v1 , X2/v2) simultaneously, and a class of admiusssuiballe estimators in the class ofmixed estimators of (β1, β2) are derived. Finally the results are extendedto some subclass of exponential family