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Simultaneous closeness among order statistics to population quantiles. (English) Zbl 1188.62164
Summary: We derive expressions for the probability that an individual order statistic is closest to the target parameter among the order statistics from a complete random sample. Results are given for random variables with bounded and complete support. We then apply these general results to location-scale parameter families of distributions with specific applications to estimation of percentiles. In this case, simultaneous-closeness probabilities depend upon the parameters through the value of \(p\) in the percentile and the sample size, \(n\). The results are finally illustrated with the estimation of percentiles for normal and exponential distributions.

62G30 Order statistics; empirical distribution functions
62G05 Nonparametric estimation
62F10 Point estimation
Full Text: DOI
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