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On extropy properties of record ranked set sampling

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Abstract

Record ranked set sampling is a ranked set sampling procedure and is used for generating record data. In this paper we have considered the information content of record ranked set sampling (\(\textit{RRSS}\)) in terms of extropy measure. We have compared \(\textit{RRSS}\) with simple random sampling for various distributions. We also obtained an expression for discrimination information measure among \(\textit{RRSS}\) and simple random sampling data for extropy measure.

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References

  1. Ahmed, A.N., Alzaid, A., Bartoszewicz, J., Kochar, S.C.: Dispersive and superadditive ordering. Adv. Appl. Probab. 18(4), 1019–22 (1986). https://doi.org/10.1017/S000186780001627X

    Article  MathSciNet  Google Scholar 

  2. Baratpour, S., Ahmadi, J., Arghami, N.R.: Entropy properties of record statistics. Stat. Pap. 48(2), 197–213 (2007)

    Article  MathSciNet  Google Scholar 

  3. Baratpour, S., Ahmadi, J., Arghami, N.R.: Some characterizations based on entropy of order statistics and record values. Commun. Stat. Theory Methods 36(1), 47–57 (2007)

    Article  MathSciNet  Google Scholar 

  4. Becerra, A., de la Rosa, J.I., Gonzalez, E., Pedroza, A.D., Escalante, N.I.: Training deep neural networks with non-uniform frame-level cost function for automatic speech recognition. Multimed. Tools Appl. 77, 27231–27267 (2018)

    Article  Google Scholar 

  5. Chandler, K.N.: The distribution and frequency of record values. J. R. Stat. Soc. Ser. B (Methodol.) 14, 220–228 (1952)

    Article  MathSciNet  Google Scholar 

  6. Chen, Z., Bai, Z.D., Sinha, B.K.: Ranked Set Sampling: Theory and Applications. Springer, New York (2004)

    Book  Google Scholar 

  7. Frank, L., Sanfilippo, G., Agro, G.: Extropy: complementary dual of entropy. Stat. Sci. 30(1), 40–58 (2015)

    MathSciNet  Google Scholar 

  8. Jozani, M.J., Ahmadi, J.: On uncertainty and information properties of ranked set samples. Inf. Sci. 264, 291–301 (2014)

    Article  MathSciNet  Google Scholar 

  9. Eskandarzadeh, M., Tahmasebi, S., Afshari, M.: Information measures for record ranked set samples. Cienc. Nat. 38(2), 554–563 (2016)

    Google Scholar 

  10. Irshad, M.R., Maya, R.: Non-parametric log kernel estimation of extropy function. Chil. J. Stat. 13, 155–163 (2022)

    MathSciNet  Google Scholar 

  11. Marshall, A.W., Olkin, I.: Life Distributions: Structure of Non-parametric, Semi-parametric, and Parametric Families. Springer (Springer Series in Statistics), New York (2007)

    Google Scholar 

  12. Martinas, K., Frankowicz, M.: Extropy-reformulation of the entropy principle. Period. Polytech. Chem. Eng. 44, 29–38 (2000)

    Google Scholar 

  13. Maya, R., Irshad, M.R., Bakouch, H., Krishnakumar, A., Qarmalah, N.: Kernel estimation of the extropy function under \(\alpha \)-mixing dependent data. Symmetry 15(4), 796 (2023). https://doi.org/10.3390/sym15040796

    Article  Google Scholar 

  14. McIntyre, G.A.: A method for unbiased selective sampling, using ranked sets. Aust. J. Agric. Res. 3(4), 385–390 (1952)

    Article  Google Scholar 

  15. Proschan, R., Barlow, F.: Statistical Theory of Reliability and Life Testing, Probability Model. Holt, Rinehart and Winnston, New York (2018)

    Google Scholar 

  16. Qiu, G., Wang, L., Wang, X.: On extropy properties of mixed systems. Probab. Eng. Inf. Sci. 33(3), 471–486 (2019)

    Article  MathSciNet  Google Scholar 

  17. Qiu, G.: Extropy of order statistics and record values. Stat. Probab. Lett. 120, 52–60 (2017)

    Article  MathSciNet  Google Scholar 

  18. Qiu, G., Eftekharian, A.: Extropy information of maximum and minimum ranked set samples with unequal samples. Commun. Stat. Theory Methods (2020). https://doi.org/10.1080/03610926.2019.1678640

    Article  Google Scholar 

  19. Raqab, M.Z., Qiu, G.: On extropy properties of ranked set sampling. Statistics 53(1), 210–226 (2019)

    Article  MathSciNet  Google Scholar 

  20. Salehi, M., Ahmadi, J.: Record ranked set sampling scheme. Metron 72, 351–365 (2019)

    Article  MathSciNet  Google Scholar 

  21. Salehi, M., Ahmadi, J.: Estimation of stress-strength reliability using record ranked set sampling scheme from the exponential distribution. JSTOR 29(5), 1149–1162 (2015)

    MathSciNet  Google Scholar 

  22. Salehi, M., Ahmadi, J., Dey, S.: Comparison of two sampling schemes for generating record-breaking data from the proportional hazard rate models. Commun. Stat. Theory Methods (2015). https://doi.org/10.1080/03610926.2014.909938

    Article  Google Scholar 

  23. Sadeghpour, A., Salehi, M., Ahmadi, J.: Estimation of the stress-strength reliability using lower record ranked set sampling scheme under the generalized exponential distribution. J. Stat. Comput. Simul. 90(1), 51–74 (2020)

    Article  MathSciNet  Google Scholar 

  24. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–432 (1948)

    Article  MathSciNet  Google Scholar 

  25. Shaked, M., Shanthikumar, J.G.: Stochastic Orders. Springer, New York (2007)

    Book  Google Scholar 

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Acknowledgements

The authors express their gratefulness for the constructive criticism of the learned referees which helped to improve considerably the revised version of the paper.

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Correspondence to R. Maya.

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Irshad, M.R., Archana, K., Maya, R. et al. On extropy properties of record ranked set sampling. Ricerche mat (2024). https://doi.org/10.1007/s11587-024-00869-2

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