Shrinkage testimation of the shape parameter of an inverse Gaussian distribution using a (α + β)min test

In this paper, we propose a shrinkage testimator for the shape parameter λ of an Inverse Gaussian distribution when the estimated value of λ is available in such a way that either λ = λ1 or λ = λ2(>;λ1) is expected. The (α + β)min test for testing the hypothesis H0: λ = λ1 against H1: λ = λ2 is derived. The shrinkage factors are chosen to be the function of the (α + β)min test. The shrinkage testimator is found to be more efficient (in the sense of the MSE) than the UMVUE in certain parametric space.