A comparison of estimators for the proportion in the tail of a normal distribution |
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Authors: | S Md-Yusof S E Rigdon |
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Institution: | 1. School of Education, Southern Illinois University at Edwardsville, 62026, Edwardsville, Illinois, USA 2. Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, 62026, Edwardsville, Illinois, USA
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Abstract: | Three estimators of the proportion in a tail of the normal distribution are compared using the criteria of mean squared error and mean absolute error. The estimators that we compare are the maximum likelihood estimator, the minimum variance unbiased estimator, and an intuitive estimator that is frequently used in practice. The intuitive estimator is similar to the MLE but uses the usual unbiased estimator of σ2 rather than the MLE of σ2. We show that the intuitive estimator has low efficiency, and for this reason it is not recommended. For very smallp and for largep the MVUE has the highest efficiency. The MLE is best for moderate values ofp. |
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