Interval estimation for inverse Gaussian distribution

In this paper, we consider interval estimation for the inverse Gaussian (IG) distribution. Using generalized pivotal quantity method, we derive the generalized confidence intervals (GCIs) for the model parameters and some quantities such as the quantile, the reliability function of the lifetime, the failure rate function, and the mean residual lifetime. We verify that the GCI of the scale parameter is the same as its commonly used exact CI. We also obtain the generalized prediction intervals (GPIs) for future failure times based on the observed failure data set. In addition, we get the GCI for the reliability of the stress-strength model when the stress and strength variables follow the IG distributions with different parameters. We compare the proposed GCIs and GPIs with the Wald CIs and bootstrap-p CIs by simulation. The simulation results show that the proposed GCIs and GPIs are superior to the Wald CIs and the bootstrap-p CIs in terms of the coverage probability. Finally, two examples are used to illustrate the proposed procedures.