Parameter and quantile estimation for the three-parameter gamma distribution based on statistics invariant to unknown location |
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Authors: | Hideki Nagatsuka N Balakrishnan |
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Institution: | 1. Faculty of System Design, Tokyo Metropolitan University, Asahigaoka 6-6, Hino-shi, Tokyo 191-0065, Japan;2. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 |
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Abstract: | The three-parameter gamma distribution is widely used as a model for distributions of life spans, reaction times, and for other types of skewed data. In this paper, we propose an efficient method of estimation for the parameters and quantiles of the three-parameter gamma distribution, which avoids the problem of unbounded likelihood, based on statistics 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 bias and mean squared error. Finally, we present two illustrative examples. |
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Keywords: | Maximum likelihood estimators Modified moment estimators Bayesian likelihood estimators Order statistics Threshold parameter Consistency |
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