This paper considers two flexible classes of omnibus goodness-of-fit tests for the inverse Gaussian distribution. The test statistics are weighted integrals over the squared modulus of some measure of deviation of the empirical distribution of given data from the family of inverse Gaussian laws, expressed by means of the empirical Laplace transform. Both classes of statistics are connected to t...

Michael, Schucany & Haas (1976) presented a method for the simulation of random variates using transformations with multiple roots. A generalization of this method to include vectorvalued transformations is given here. A short introduction to the inverse Gaussian distribution is given. The joint distribution of the sufficient statistic is well known, but the proof given here based on the Basu t...

We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed are weighted $L^2$-type depending on tuning parameter. develop asymptotic theory under null hypothesis and broad alternative distributions. These results used to show that parametric bootstrap procedure, which we employ implement test, is asymptotically valid whole test procedure consistent. A co...

Linear inverse Gaussian problems is traditionally solved using least squares based inversion. The center of the posterior Gaussian probability distribution is often chosen as the solution to such problems, while the solution is in fact the posterior Gaussian probability distribution itself. We present an algorithm, based on direct sequential simulation, which can be used to efficiently draw sam...