Computational Approach Test using Likelihood Based Tests for the Equality of Inverse Gaussian Means

Abstract

In this study, we propose three different test procedures by plugging the Wald (W), score (S) and likelihood ratio (LR) statistics into the computational approach test (CAT) to test the equality of inverse Gaussian means when the scale parameters are unknown and arbitrary. Restricted maximum likelihood (RML) estimators are used in developing the proposed test procedures. Since the RML estimators cannot be derived in closed-form, the bisection method is used to obtain the numerical solutions. The motivation behind using the CAT procedure is that it can easily be implemented to hypothesis testing problems without knowing the sampling distributions of the test statistics. The proposed and existing procedures are compared in terms of type I error rates and powers via an extensive Monte Carlo simulation study. In addition, a real data set is analyzed for illustration.

Keywords

• computational approach test
• score test
• wald test
• likelihood ratio test
• inverse Gaussian distribution