Interval estimation for the exponential inverse Gaussian distribution

Abstract

Exact confidence intervals may be theoretically feasible for some problems but they can be difficult to obtain in practice as is often the case when there are nuisance parameters present. Consequently, likelihood-based interval estimation methods are often used in applied work. The loss in accuracy when approximate intervals are used is not necessarily a serious issue especially when we derive such intervals from O(n-3/2) accurate results like those in, for example, Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple general formula for tail probabilities for frequentist and bayesian inference. Biometrika, 86(2), 249-264. In this article, we obtain third-order accurate approximate confidence..