Maximum likelihood predictive densities for the inverse Gaussian distribution with applications to reliabiltiy and lifetime predictions

摘要

Maximum likelihood predictive densities (MLPD) for the inverse Gaussian distribution are derived for the cases of one or both parameters unknown. They are then aplied to obtain estimators of the reliability function and prediction or shortest prediction intervals for a future observaton. 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, adn 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.