Maximum Likelihood Predictive Densities for the Inverse Gaussian Distribution with Applications to Reliability and Lifetime Predictions

Maximum likelihood predictive densities (MLPD) for the inverse Gaussian distribution are derived for the cases of one or both parameters unknown. They are then applied to obtain estimators of the reliability function and prediction or shortest prediction intervals for a future observation. Comparisons with the existing likelihood or frequentist methods show that the MLPD estimators of reliability gives smaller bias and smaller MSE for a wide range of population values, and that the MLPD prediction intervals are shorter while preserving the correct coverage probability. The shortest MLPD prediction intervals further sharpen the above equitailed MLPD intervals in terms of interval lengths.