Asymptotic Confidence Ellipses of Parameters for the Inverse Gaussian Distribution

Abstract In this article, we derive maximum likelihood equations and find Fisher information matrix to construct asymptotic confidence ellipses for parameters of the inverse Gaussian distribution. We use the coverage probabilities to compare with the confidence coefficient of 0.98. The investigation of the accuracy of the confidence ellipses are fulfilled via the Monte Carlo method.  Four cases of sample sizes  (30, 100, 500, and 1,000) and six cases of  are investigated at parameter  which is set to be 1.  R (2.15.2) software is used for our simulation study with 10,000 iterations. The results are as follows. The coverage probabilities of confidence ellipses for parameters of the inverse Gaussian distribution increase when sample size  is increased.  They are also close to the confidence coefficient of 0.98 for all values of both parameters. In addition, the various values of the parameter  when  is 1 of the inverse Gaussian distribution give high coverage probabilities when  is large. Keywords : Maximum Likelihood Estimate; Simultaneous Confidence Interval; Skewed Distribution.