Testing homogeneity of inverse Gaussian scale-like parameters: a saddlepoint approach

The cumulant generating function of the statistic W defined in Chang et al. (Stat Probab Lett 82:1755–1760, 2012 ) for testing homogeneity of the scale-like parameters of several inverse Gaussian distributions is derived in this paper. Then two saddlepoint-based methods are proposed to obtain the asymptotic distribution function of W . Simulation results illustrate that the proposed methods are very accurate and powerful even for very small sample sizes and large number of populations.