Goodness-of-fit tests for inverse Gaussian distribution in the presence and absence of censoring

Abstract

In this article, we use the fixed point characterization for inverse Gaussian distribution to develop goodness of fit tests for the same. First, we propose a test for inverse Gaussian distribution when the data is complete. We then discuss, how the test procedure can be modified to incorporate right-censored observations. We use U-statistics theory to develop the test statistic. The large sample behaviour of the proposed test statistics for both uncensored and censored data are studied. We conduct extensive Monte Carlo simulation studies to validate the finite sample behaviour of the proposed tests. The practical usefulness of the tests is illustrated using real data sets. We also propose a new jackknife empirical likelihood ratio test for the inverse Gaussian distribution with unit parameters.