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The problem of estimating positive powers of scale parametershas been considered under order restriction when samples are available from two normal populations with a common mean  μ . Maximum-likelihood estimators and several plug-in type estimators using some popular estimators of the common mean have been proposed. Sufficient conditions for improving equivariant estimators for the positive powers of the scale parameters under order restriction have been derived. Consequently, several improved estimators have been proposed. A numerical comparison among all the proposed estimators in the special cases ( c  = 1 and) has been made in terms of risk values using the quadratic loss function, and recommendations are given for the use of the estimators. Finally, a real-life example has been considered to show the potential application of the model problem.

Estimating positive powers of the scale parameters under order restriction for two normal populations with a common mean