A method for estimating parameters and quantiles of the three-parameter inverse Gaussian distribution based on statistics invariant to unknown location

Abstract

The inverse Gaussian (IG) distribution, also known as the Wald distribution, is a long-tailed positively skewed distribution and a well-known lifetime distribution. In this paper, we propose an efficient method of estimation for the parameters and quantiles of the three-parameter IG distribution, which is based on statistics invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared with other prominent methods in terms of bias and variance. Finally, we present two illustrative examples.

Keywords:

• maximum-likelihood estimators
• mixed-moments method
• conditional method of moments
• order statistics
• threshold parameter
• quantile

AMS Subject Classification:

• 62F10
• 62F86

Acknowledgements

We express our sincere thanks to the Editor, the Associate Editor and the two reviewers for their comments that greatly improved this paper. Hideki Nagatsuka was partially supported by the Grant-in-Aid for Young Scientists (B) 24710170, the Ministry of Education, Culture, Sports, Science and Technology, Japan, which made his visit to McMaster University, Canada, possible.