Parameter and quantile estimation for the three-parameter lognormal distribution based on statistics invariant to unknown location

Abstract

Lognormal distribution is one of the popular distributions used for modelling positively skewed data, especially those encountered in economic and financial data. In this paper, we propose an efficient method for the estimation of parameters and quantiles of the three-parameter lognormal distribution, which avoids the problem of unbounded likelihood, by using statistics that are invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared to other prominent methods in terms of both bias and mean-squared error. Finally, we present two illustrative examples.

Keywords:

• maximum likelihood estimators
• modified moment estimators
• local maximum likelihood estimators
• order statistics
• threshold parameter
• quantile

AMS Subject Classifications :

• 62F10
• 62F86

Acknowledgements

We express our sincere thanks to the editor, the associate editor and the reviewer for their comments that greatly improved this paper. Hideki Nagatsuka was partially supported by the Grant-in-Aid for Young Scientists (B) 21710155, The Ministry of Education, Culture, Sports, Science and Technology, Japan, which enabled his visit to McMaster University, Canada.