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Pitman closeness of record values to population quantiles. (English) Zbl 1171.62033
Summary: We examine the Pitman closeness of record statistics to the population quantiles of a location-scale family of distributions and study its monotonicity properties. Even though in general it depends on the parent distribution, exact expressions are derived for the required probabilities in the case of uniform (\(- 1,1\)) and exponential distributions. For the population median, it is shown that the first upper record is the Pitman-closest among all upper record values. Moreover, for the population median, in the case of symmetric distributions, the Pitman closeness probabilities of records are shown to be distribution-free and explicit expressions are also derived for these probabilities.

62G32 Statistics of extreme values; tail inference
62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions
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