zbMATH — the first resource for mathematics

Nonparametric confidence and tolerance intervals from record values data. (English) Zbl 1050.62053
Summary: In a number of situations only observations that exceed or only those that fall below the current extreme value are recorded. Examples include meteorology, hydrology, athletic events and mining. Industrial stress testing is also an example in which only items that are weaker than all the observed items are destroyed.
In this paper, it is shown that how record values can be used to provide distribution-free confidence intervals for population quantiles and tolerance intervals. We provide some tables that help one choose the appropriate record values and present a numerical example. Also universal upper bounds for the expectation of the length of the confidence intervals are derived. The results may be of interest in situations where only record values are stored.

MSC:
 62G15 Nonparametric tolerance and confidence regions 62G32 Statistics of extreme values; tail inference
Full Text:
References:
 [1] Ahmadi, J. and Arghami, N. A. (2001) On the Fisher information in record values,Metrika 53, 3, 195–206. · Zbl 0990.62044 [2] Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992)A first course in order statistics, John Wiley, New York. · Zbl 0850.62008 [3] Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998)Records, John Wiley, New York. [4] Carlin, P. B. and Gelfand, A. E. (1993) Parametric likelihood inference for record breaking problems,Biometrika, 80, 3, 507–515. · Zbl 0800.62110 [5] Feuerverger, A. and Hall, P. (1998) On statistical inference based on record values,Extermes, 12, 169–190. · Zbl 0923.62039 [6] Glick, N. (1978) Breaking record and breaking boards.Amer. Math. Monthly, 85, 2–26. · Zbl 0395.62040 [7] Gulati, S. and Padgett, W. J. (1994) Smooth nonparametric estimation of the distribution and density functions from record-breaking data,Comm. Stat.-Theory Methods, 23(5), 1259–1274. · Zbl 0825.62160 [8] Serfling, R. J. (1980)Approximation Theorems of Mathematical Statistics, Wiley, New York. · Zbl 0538.62002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.