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Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records

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  • Elham Basiri
  • Jafar Ahmadi

Abstract

In this paper, we consider the prediction problem in two-sample case and study the non-parametric predicting future progressively Type-II censored order statistics based on observed $$k$$ k -records from the same distribution. Also, prediction intervals for progressively Type-II censored spacings are obtained based on $$k$$ k -record spacings. It is shown that the coverage probabilities of these intervals are exact and do not depend on the underlying distribution. Moreover, optimal prediction intervals are derived for each case. Finally, for illustrating the proposed procedure, we consider a real data set and numerical computations are given. The results of Ahmadi and Balakrishnan (Statistics 44:417–430, 2010 ) can be achieved as special cases of our results. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Elham Basiri & Jafar Ahmadi, 2013. "Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records," Computational Statistics, Springer, vol. 28(6), pages 2825-2848, December.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2825-2848
    DOI: 10.1007/s00180-013-0430-9
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    References listed on IDEAS

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    1. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    2. Jafar Ahmadi & Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2009. "Prediction of k-records from a general class of distributions under balanced type loss functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 19-33, June.
    3. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    4. Balakrishnan, N. & Burkschat, Marco & Cramer, Erhard & Hofmann, Glenn, 2008. "Fisher information based progressive censoring plans," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 366-380, December.
    5. Essam Al-Hussaini & Abd Ahmad, 2003. "On Bayesian interval prediction of future records," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 79-99, June.
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    Cited by:

    1. Elham Mirfarah & Jafar Ahmadi, 2014. "Pitman closeness of $$k$$ k -records from two sequences to progressive Type-II censored order statistics," Computational Statistics, Springer, vol. 29(5), pages 1279-1300, October.

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