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.