Percentile Estimation in Inverse Gaussian Distributions

Abstract

This paper presents procedures for percentile estimation in the three-parameter inverse Gaussian (IG3) and the two-parameter inverse Gaussian (IG2) distributions. All procedures require first the estimation of distribution parameters and second the computation of the desired quantile at the estimated parameters. Parameter estimation is accomplished by maximum likelihood (ML) or a mixed moments (MXM) method. A Newton-Rahpson (NR) procedure is used for inverting the CDF. Simulation and asymptotic results are given for the resulting estimators. Two sets of real data are used to illustrate the procedures.

Keywords:

• Inverse Gaussian distribution
• Maximum likelihood
• Mixed moments procedure
• Quantile estimation
• Shifted gamma approximations

Mathematical Subject Classification:

• 62F10
• 62F12
• 62F25
• 60-08