A note on the exact prediction limits for future observations from the inverse gaussian distribution

Abstract

Through use of a result established by Tweedie (1957a), exact prediction interval for the mean of future observations can be derived straightforwardly. The conditions for which the exact prediction limits are two-sided are studied. The comparison of two-sided intervals among Padgett's approximation, Chhikara and Guttman frequentist approach and the exact inference developed here is made via extensive Monte Carlo simulations. In most simulation cases, the exact two-sided intervals (for the mean of future observations) obtained in this article are superior in terms of larger estimated coverage probabilities and shorter estimated average lengths. A summary and recommendation of the construction of two-sided prediction intervals for the mean of future observations from the inverse Gaussian distribution is included.

Keywords:

• Inverse Gaussian
• maximum likelihood estimates
• factorization
• prediction interval