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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References
Brown, G.G. and Rutemiller, H.C. (1973), “The efficiencies of maximum likelihood and minimum variance unbiased estimators of fraction defective in the normal case,”Technometrics, 15, pp. 849–855.
Gitlow, H., Gitlow, S., Oppenheim, A., and Oppenheim, R. (1989)Tools and Methods for the Improvement of Quality, Irwin: Homewood, IL.
Hecht, H. (1990),Mathematics in Chemistry, Prentice Hall: New York.
Lieberman, G. and Resnikoff, G. (1955), “Sampling plans for inspection by variables,”Journal of the American Statistical Association, 50, pp. 457–516.
Montgomery, D. (1990),Introduction to Statistical Quality Control, Second Ed., Wiley: New York.
Zacks, S. and Milton, R. C. (1971), “Mean square errors of the best unbiased and maximum likelihood estimators of tail probabilities in normal distributions,”Journal of the American Statistical Association, 66, pp. 590–593.
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Md-Yusof, S., Rigdon, S.E. A comparison of estimators for the proportion in the tail of a normal distribution. Statistical Papers 33, 33–38 (1992). https://doi.org/10.1007/BF02925310
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DOI: https://doi.org/10.1007/BF02925310