Inverse Gaussian distribution.

13 Let X1,..., Xn be a sample from the inverse Gaussian distribution I(μ, τ ), both parameters unknown.

(i) There exists a UMP unbiased test of μ ≤ μ0 against μ > μ0, which rejects when X¯ > C[

(Xi + 1/Xi)], and a corresponding UMP unbiased test of μ = μ0 against μ0 = μ0.

[The conditional distribution needed to carry out this test is given by Chhikara and Folks (1976).]

13 For additional information conc

(ii) There exist UMP unbiased tests of H : τ = τ0 against both one- and two-sided hypotheses based on the statistic V = (1/Xi − 1/X¯).
(iii) When τ = τ0, the distribution of τ0V is χ2 n−1.
[Tweedie (1957).]