Modified signed log-likelihood test for the coefficient of variation of an inverse Gaussian population

In this paper, we consider the problem of two sided hypothesis testing for the parameter of coefficient of variation of an inverse Gaussian population. An approach used here is the modified signed log-likelihood ratio (MSLR) method which is the modification of traditional signed log-likelihood ratio test. Previous works show that this proposed method has third-order accuracy whereas the traditional approach has first-order one. Indeed, these methods are based on likelihood with a higher order of accuracy. For this reason, we are interested in using this method for inference about the parameter of coefficient of variation of an inverse Gaussian distribution. All necessary formulas for obtaining MSLR statistic are provided. Numerically, the performances of this method are compared with classical approaches, in terms of empirical type-I error rate and empirical test power. Simulation results show that the empirical type-I error rates of MSLR are close to nominal type-I error rate, even for small sample sizes whereas the traditional approaches are reliable only for large sample sizes. Comparing the empirical power sizes shows that the power of MSLR method is superior to other considered methods in some settings, by regarding that the competing approaches cannot perform well in controlling the type-I error probability because their empirical type-I error rates are far from the nominal type-I error rate. Finally, we illustrate the proposed methods using a real data set and then we conclude the paper.