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On Pitman’s measure of closeness of \(k\)-records. (English) Zbl 1221.62074
Summary: Pitman closeness of both the upper and lower \(k\)-record statistics to the population quantiles of a location-scale family of distributions is studied. For the population median, the Pitman-closest \(k\)-record is also determined. In the case of symmetric distributions, the Pitman closeness probabilities of \(k\)-record statistics are shown to be distribution-free, and explicit expressions are also derived for these probabilities. Exact expressions are derived for the required probabilities for uniform and exponential distributions. Numerical results are given for these families and also the Pitman-closest \(k\)-record is determined.

MSC:
62G32 Statistics of extreme values; tail inference
62G05 Nonparametric estimation
62E15 Exact distribution theory in statistics
65C60 Computational problems in statistics (MSC2010)
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