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Current k-records and their use in distribution-free confidence intervals

Author

Listed:
  • Ahmadi, J.
  • Razmkhah, M.
  • Balakrishnan, N.

Abstract

In a sequence of independent and identically distributed (iid) random variables, the kth largest (smallest) observation in a partial sample is well-known as the upper (lower) k-record value, when its value is greater (smaller) than the corresponding observation in the previous partial sample. In this paper, we consider the k-record statistics at the time when the nth k-record of any kind (either an upper or lower) is observed, termed as current k-records. We derive a general expression for the joint probability density function (pdf) of these current k-records and use it to construct distribution-free confidence intervals for population quantiles. It is shown that the expected width of these confidence intervals is decreasing in k and increasing in n. We also discuss the construction of tolerance intervals and limits in terms of current k-records. Finally, a numerical example is presented to illustrate all the methods of inference developed here.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:1:p:29-37
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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.
    2. 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.
    3. 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.
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    Cited by:

    1. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    2. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.

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