Skip to main content
Log in

Record ranked set sampling scheme

  • Published:
METRON Aims and scope Submit manuscript

Abstract

A new sampling scheme for generating record-breaking data is introduced and called record ranked set sampling (RRSS). A distribution-free two-sided prediction interval for future order statistics based on RRSS is derived. Numerical computations are obtained for comparing the results with the case based on ordinary records. Also, confidence intervals for quantiles of the parent distribution and prediction intervals for the ordinary records are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Ahmadi, J., Arghami, N.R.: Some univariate stochastic orders on record values. Commun. Stat. Theory Methods 30, 69–74 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahmadi, J., Doostparast, M.: Bayesian estimation and prediction for some life distributions based on record values. Stat. Pap. 47, 373–392 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahmadi, J., Balakrishnan, N.: Prediction of order statistics and record values from two independent sequences. Statistics 44, 417–430 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: Records. Wiley, New York (1998)

    Book  MATH  Google Scholar 

  5. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: A first course in order statistics. Unabridged republication of the 1992 original. In: Classics in Applied Mathematics, vol. 54. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2008)

  6. Balakrishnan, N., Li, T.: Ordered ranked set samples and applications to inference. Ann. Inst. Stat. Math. 58, 757–777 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Balakrishnan, N., Kamps, U., Kateri, M.: Minimal repair under a step-stress test. Stat. Probab. Lett. 79, 1548–1558 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Balakrishnan, N., Beutner, E., Cramer, E.: Computational aspects of statistical intervals based on two Type-II censored samples. Comput. Stat. 28, 893–917 (2013)

    Google Scholar 

  9. Beutner, E., Cramer, E.: Nonparametric meta-analysis for minimal-repair systems. Aust. N. Z. J. Stat. 52, 383–401 (2010)

    Article  MathSciNet  Google Scholar 

  10. Brown, M., Proschan, F.: Imperfect repair. J. Appl. Probab. 20, 851–859 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  11. David, H.A., Nagaraja, H.N.: Order Statistics, 3rd edn. Wiley, Hoboken (2003)

    Book  MATH  Google Scholar 

  12. Gupta, R.C., Kirmani, S.N.U.A.: Closure and monotonicity properties of nonhomogeneous Poisson processes and record values. Probab. Eng. Inf. Sci. 2, 475–484 (1988)

    Article  MATH  Google Scholar 

  13. Kaminsky, K.S., Nelson, P.I.: Prediction of order statistics. In: Balakrishnan, N., Rao, C.R. (eds.) Handbook of Statistics—17: Order Statistics: Applications, pp. 431–450. North-Holland, Amsterdam (1998)

    Chapter  Google Scholar 

  14. McIntyre, G.A.: A method for unbiased selective sampling, using ranked sets. Aust. J. Agric. Res. 3, 385–390 (1952)

    Article  Google Scholar 

  15. Proschan, F.: Theoretical explanation of observed decreasing failure rate. Technometrics 5, 375–383 (1963)

    Article  Google Scholar 

  16. Salehi, M., Ahmadi, A., Balakrishnan, N.: Prediction of order statistics and record values based on ordered ranked set sampling. J. Stat. Comput. Simul. (2013). doi:10.1080/00949655.2013.803194

Download references

Acknowledgments

The authors would like to thank the AE and two referees for their valuable suggestions and constructive comments.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jafar Ahmadi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salehi, M., Ahmadi, J. Record ranked set sampling scheme. METRON 72, 351–365 (2014). https://doi.org/10.1007/s40300-014-0038-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40300-014-0038-z

Keywords

Mathematics Subject Classification (2010)

Navigation