On the common mean of several inverse Gaussian distributions based on a higher order likelihood method

An interval estimation method for the common mean of several heterogeneous inverse Gaussian (IG) populations is discussed. The proposed method is based on a higher order likelihood-based procedure. The merits of the proposed method are numerically compared with the signed log-likelihood ratio statistic, two generalized pivot quantities and the simple t-test method with respect to their expected lengths, coverage probabilities and type I errors. Numerical studies show that the coverage probabilities of the proposed method are very accurate and type I errors are close to the nominal level.05 even for very small samples. The methods are also illustrated with two examples.