Journal of Computational and Applied Mathematics vol:186 issue:1 pages:268-282
Let X-1 and X-2 be two independent random variables representing the populations II1 and II2, respectively, and suppose that the random variable Xi has a gamma distribution with shape parameter p, same for both the populations, and unknown scale parameter theta(i), i = 1, 2. Define, M = 1, if X-1 > X-2, M = 2, if X-2 > X-1 and J = 3 - M. We consider the component wise estimation of random parameters theta(M) and theta(j), under the scale invariant squared error loss functions L-1 ((theta) under bar, delta(1)) = (delta(1)/theta(M) - 1)(2) and L-2((theta) under bar, delta(2)) = (delta(2)/theta(J) - 1)(2), respectively. Sufficient conditions for the inadmissibility of equivariant estimators of theta(M) and theta(J) are derived. As a consequence, various natural estimators are shown to be inadmissible and better estimators are obtained.