Modified Moment Estimation for the Three-Parameter Inverse Gaussian Distribution

Abstract

A modification of moment estimators, in which the third moment is replaced by a function of the first order statistic, is presented for the mean, variance, shape, and threshold parameters of the three-parameter inverse Gaussian distribution. The modified moment estimators retain the unbiased property of moment estimators with respect to distribution mean and variance while achieving a reduction in both bias and variance of the distribution shape parameter. Their properties also compare favorably with the maximum likelihood estimators. Calculations are made easy with the aid of accompanying tables and a chart. Two illustrative examples are included.

• Inverse Gaussian Distribution
• Parameter Estimation

Additional information

Notes on contributors

A. Clifford Cohen

Dr. Cohen is an Emeritus Professor in the Department of Statistics. He is a Founding Member and a Fellow of ASQC.

Betty Jones Whitten

Dr. Whitten is an Associate Professor in the Department of Quantitative Business Analysis.