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Confidence intervals for quantiles in terms of record range

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  • Ahmadi, J.
  • Balakrishnan, N.

Abstract

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. In this paper, 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.

Suggested Citation

  • Ahmadi, J. & Balakrishnan, N., 2004. "Confidence intervals for quantiles in terms of record range," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 395-405, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:395-405
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    References listed on IDEAS

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    1. J. Ahmadi & N. Arghami, 2003. "Nonparametric confidence and tolerance intervals from record values data," Statistical Papers, Springer, vol. 44(4), pages 455-468, October.
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    Citations

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    Cited by:

    1. Ahmadi, Jafar & Fashandi, M., 2009. "Some characterization and ordering results based on entropies of current records," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2053-2059, October.
    2. Ahmadi, J. & Balakrishnan, N., 2005. "Distribution-free confidence intervals for quantile intervals based on current records," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 190-202, December.
    3. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    4. S. Baratpour & J. Ahmadi & N. Arghami, 2007. "Entropy properties of record statistics," Statistical Papers, Springer, vol. 48(2), pages 197-213, April.
    5. Ahmadi, Jafar & Balakrishnan, N., 2010. "Pitman closeness of current records for location-scale families," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1577-1583, November.
    6. Jazaa S. Al-Mutairi & Mohammad Z. Raqab, 2020. "Confidence intervals for quantiles based on samples of random sizes," Statistical Papers, Springer, vol. 61(1), pages 261-277, February.
    7. Ahmadi, J. & Razmkhah, M. & Balakrishnan, N., 2009. "Current k-records and their use in distribution-free confidence intervals," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 29-37, January.
    8. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    9. Ahmadi, J. & Balakrishnan, N., 2008. "Nonparametric confidence intervals for quantile intervals and quantile differences based on record statistics," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1236-1245, August.
    10. Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    11. Mohammad Raqab, 2009. "Distribution-free prediction intervals for the future current record statistics," Statistical Papers, Springer, vol. 50(2), pages 429-439, March.
    12. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.
    13. M. Emadi & J. Ahmadi & N. Arghami, 2007. "Comparison of record data and random observations based on statistical evidence," Statistical Papers, Springer, vol. 48(1), pages 1-21, January.

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