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>

For estimating an unknown scale parameter of Gamma distribution, we introduce the use of an asymmetric scale invariant loss function reflecting precision of estimation. This loss belongs to the class of precautionary loss functions. The problem of estimation of scale parameter of a Gamma...