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Prediction intervals for future records

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  • Raqab, Mohammad Z.
  • Balakrishnan, N.

Abstract

Suppose upper records were observed from a X-sequence of iid continuous random variables, and that another independent Y-sequence of iid variables from the same distribution is to be observed. In this paper, we then derive various exact distribution-free prediction intervals for records from the Y-sequence based on the record values from the X-sequence. Specifically, distribution-free prediction intervals for individual records as well as outer and inner prediction intervals are derived based on X-records, and exact expressions for the coverage probabilities of these intervals are also derived. A data representing the records of temperatures is used to illustrate all the results developed here.

Suggested Citation

  • Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1955-1963
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    1. 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.
    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.
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    1. MirMostafaee, S.M.T.K. & Ahmadi, Jafar, 2011. "Point prediction of future order statistics from an exponential distribution," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 360-370, March.
    2. Balakrishnan, N. & Kamps, U. & Kateri, M., 2009. "Minimal repair under a step-stress test," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1548-1558, July.
    3. Jafar Ahmadi & N. Balakrishnan, 2012. "Outer and inner prediction intervals for order statistics intervals based on current records," Statistical Papers, Springer, vol. 53(3), pages 789-802, August.
    4. Jafar Ahmadi & N. Balakrishnan, 2013. "On the nearness of record values to order statistics from Pitman’s measure of closeness," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 521-541, May.
    5. S. MirMostafaee & Jafar Ahmadi & Narjes Sadeghian, 2015. "Pitman closeness of predictors of future order statistics for two parameter exponential distribution," Computational Statistics, Springer, vol. 30(4), pages 1163-1183, December.
    6. Mohammad Raqab & Jafar Ahmadi & Byan Arabli, 2013. "Comparisons among some predictors of exponential distributions using Pitman closeness," Computational Statistics, Springer, vol. 28(5), pages 2349-2365, October.
    7. Ahmadi, J. & MirMostafaee, S.M.T.K., 2009. "Prediction intervals for future records and order statistics coming from two parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 977-983, April.
    8. Bagheri, S.F. & Asgharzadeh, A. & Basiri, E. & Fernández, A.J., 2019. "One-sample prediction regions for future record intervals," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 15-20.
    9. Ahmadi, Jafar & MirMostafaee, S.M.T.K. & Balakrishnan, N., 2010. "Nonparametric prediction intervals for future record intervals based on order statistics," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1663-1672, November.

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