Distribution-free confidence intervals for quantiles and tolerance intervals in terms of k-records

Abstract

In this paper, we consider the problem of determining non-parametric confidence intervals for quantiles when available data are in the form of k-records. Distribution-free confidence intervals as well as lower and upper confidence limits are derived for fixed quantiles of an arbitrary unknown distribution based on k-records of an independent and identically distributed sequence from that distribution. The construction of tolerance intervals and limits based on k-records is also discussed. An exact expression for the confidence coefficient of these intervals are derived. Some tables are also provided to assist in choosing the appropriate k-records for the construction of these confidence intervals and tolerance intervals. Some simulation results are presented to point out some of the features and properties of these intervals. Finally, the data, representing the records of the amount of annual rainfall in inches recorded at Los Angeles Civic Center, are used to illustrate all the results developed in this paper and also to demonstrate the improvements that they provide on those based on either the usual records or the current records.

Keywords:

• confidence coefficient
• current records
• order statistics
• quantiles
• quantile intervals
• records
• record range
• tolerance intervals
• k-records

Acknowledgements

The authors would like to thank an anonymous referee and the associate editor for their useful comments and constructive criticisms on the original version of this manuscript which led to this considerably improved version.

Additional information

Notes on contributors

N. Balakrishnan

Both authors are members of the Ordered and Spatial Data Center of Excellence of Ferdowsi University of Mashhad.