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Confidence intervals for quantiles in terms of record range. (English) Zbl 1086.62064
Summary: Often, in industrial stress testing, meteorological data analysis, athletic events, and other similar situations, measurements may be made sequentially and only values larger or smaller than all previous ones are observed. When the number of records is fixed in advance, the data are referred to as inversely sampled record breaking data. We introduce some properties of current records. Distribution-free confidence intervals are derived to estimate the fixed quantiles of an arbitrary unknown distribution, based on current records of an iid sequence from that distribution. Several universal upper bounds for the expectation of the length of the confidence intervals are derived. Some tables are also provided in order to choose the appropriate records. The results may be of interest in some life testing situations.

MSC:
62G32 Statistics of extreme values; tail inference
62G15 Nonparametric tolerance and confidence regions
62G30 Order statistics; empirical distribution functions
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