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Estimation of Quantiles of Location-Scale Distributions Based on Two or Three Order Statistics
Peter Kubat and Benjamin Epstein
Vol. 22, No. 4 (Nov., 1980), pp. 575-581
Published by: Taylor & Francis, Ltd. on behalf of American Statistical Association and American Society for Quality
Stable URL: http://www.jstor.org/stable/1268195
Page Count: 7
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Linear asymptotically unbiased estimators of ξ quantiles, xξ, 0 < ξ < 1, of location-scale distributions are considered. These are based on two or three order statistics suitably selected in a neighborhood of the sample quantile X(N), N = [nξ] + 1, where n is the sample size. The estimators are easy to calculate and are substantially more efficient than the nonparametric estimator x̃ξ=X(N). The estimators are tabulated for selected values of ξ for the normal and extreme value (Gumbel) distributions. Also given are the asymptotic relative efficiencies of these estimators when compared with the maximum likelihood estimator of xξ based on all n observations.
Technometrics © 1980 American Statistical Association