Normal quantile estimation based on minimizing the error in predicted distribution functions |
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| Authors: | J.E. Angus |
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| Affiliation: | Hughes Aircraft Company , Ground Systems Group , Fullerton, California |
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| Abstract: | Estimators of the form [Xbar] + kS for estimating the p quantile of a normal distribution are studied when k is chosen to either minimize the mean square error in the predicted distribution function or to make the predicted distribution function unbiased for p. Here, [Xbar] and S are the usual sample mean and standard deviation, respectively, and the predicted distribution function is the true (normal) distribution function evaluated at the estimated quantile. These k values are presented for various sample sizes and values of p, and application to warranty determination is discussed. |
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| Keywords: | mean square error in predicted distribution function non-central t-distribution bivariate t-distribution warranties |
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