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Distribution-free confidence intervals for quantile intervals based on current records. (English) Zbl 1085.62050
Summary: Suppose we know the combined number of upper and lower records and the current values of the lower and the upper records. Then, it is shown how various exact nonparametric confidence intervals can be constructed based on this information. Such intervals are exact and distribution-free in that the corresponding coverage probabilities are known exactly without any assumption about the parent distribution other than that its distribution function is continuous.
Distribution-free outer and inner confidence intervals are obtained for quantile intervals based on current records. An exact expression for the confidence coefficient of these outer and inner confidence intervals is derived. Upper and lower confidence limits for quantile differences are obtained. A data set representing the record values of average July temperatures in Neuenburg, Switzerland, is used to illustrate the results.

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