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.