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Pitman closeness of current records for location-scale families. (English) Zbl 1195.62063

Summary: The largest and the smallest observations are considered at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. These statistics are referred to as current upper and lower records, respectively, in the statistical literature. We derive expressions for the Pitman closeness of current records to a common population parameter and then apply these results to location-scale families of distributions with special emphasis on the estimation of quantiles. In the case of symmetric distributions, we show that this criterion possesses some symmetry properties. Exact expressions are derived for the Pitman closeness probabilities in the case of Uniform\((-1,1)\) and exponential distributions. Moreover, for the population median, we show that the Pitman closeness probability is distribution-free.

MSC:

62G32 Statistics of extreme values; tail inference
62G05 Nonparametric estimation
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