Parameter and quantile estimation for the three-parameter lognormal distribution based on statistics invariant to unknown location |
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Authors: | Hideki Nagatsuka N. Balakrishnan |
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Affiliation: | 1. Faculty of System Design , Tokyo Metropolitan University , Asahigaoka 6-6, Hino-shi , Tokyo , 191-0065 , Japan hnagatsu@sd.tmu.ac.jp;3. Department of Mathematics and Statistics , McMaster University , Hamilton , Ontario , Canada , L8S 4K1 |
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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. |
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Keywords: | maximum likelihood estimators modified moment estimators local maximum likelihood estimators order statistics threshold parameter quantile |
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