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Pitman closeness of order statistics to population quantiles. (English) Zbl 1290.62025
Summary: Pitman closeness of sample order statistics to population quantiles of a location-scale family of distributions is discussed. Explicit expressions are derived for some specific families such as uniform, exponential, and power function. Numerical results are then presented for these families for sample sizes $$n = 10,15$$, and for the choices of $$p = 0.10, 0.25, 0.75, 0.90$$. The Pitman-closest order statistic is also determined in these cases and presented.

##### MSC:
 62F10 Point estimation 62G05 Nonparametric estimation 62G30 Order statistics; empirical distribution functions
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##### References:
 [1] DOI: 10.1137/1.9780898719062 · Zbl 1172.62017 [2] Balakrishnan N., Pitman Closeness of Sample Median to Population Median Classic edition (2008) [3] DOI: 10.1002/0471722162 · Zbl 1053.62060 [4] DOI: 10.1137/1.9781611971576
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