Independent random samples are taken from two normal populations with means <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mu _1$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mu _2$$</EquationSource> </InlineEquation> and a common unknown variance <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\sigma ^2.$$</EquationSource> </InlineEquation> It is known that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\mu _1\le \mu _2.$$</EquationSource> </InlineEquation> In this paper, estimation of the common standard deviation <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\sigma $$</EquationSource> </InlineEquation> is considered with respect to...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

Estimation of the entropy of several exponential distributions is considered. A general inadmissibility result for the scale equivariant estimators is proved. The results are extended to the case of unequal sample sizes. Risk functions of proposed estimators are compared numerically.