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On Some Models of Ordered Random Variables and Characterizations of Distributions

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Abstract

The concept of extended neighboring order statistics introduced in Asadi et al. (2001) is a general model containing models of ordered random variables that are included in the generalized order statistics. This model also includes several models of ordered random variables that are not included in the generalized order statistics and is a helpful tool in unifying characterization results from several models of ordered random variables. In this paper, some general classes of distributions with many applications in reliability analysis and engineering, such as negative exponential, inverse exponential, Pareto, negative Pareto, inverse Pareto, power function, negative power, beta of the first kind, rectangular, Cauchy, Raleigh, Lomax, etc., have been characterized by using the regression of extended neighboring order statistics and decreasingly ordered random variables.

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REFERENCES

  1. M. Ahsanullah and M. Z. Raqab, Characterizations of distributions by conditional expectations of generalized order statistics,’’ Appl. Stat. Sci. 13 (1), 41–48 (2004).

    MathSciNet  MATH  Google Scholar 

  2. S. E. Abu-Youssef, ‘‘On characterizations of certain distributions of record values,’’ Appl. Math. Comput. 145, 443–450 (2003).

    MathSciNet  MATH  Google Scholar 

  3. B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, A First Course in Order Statistics (Wiley, New York, 1992).

    MATH  Google Scholar 

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

    Book  Google Scholar 

  5. M. Asadi, C. R. Rao, and D. N. Shanbhag, ‘‘Some unified characterization results on the generalized pareto distribution,’’ J. Stat. Plan. Inference 93, 29–50 (2001).

    Article  MathSciNet  Google Scholar 

  6. I. Bairamov and N. Balakrishnan, ‘‘A note on regressing order statistics and record values,’’ in Advances on Models, Characterizations and Applications,’’ Ed. by I. Bairamov, N. Balakrishnan, and O. Gebizlioglu (Chapman and Hall/CRC, 2005), Ch. 7, pp. 111–120.

    Google Scholar 

  7. M. Bieniek and D. Szynal, ‘‘Characterizations of distributions via linearity of generalized order statistics,’’ Metrika 58, 259–271 (2003).

    Article  MathSciNet  Google Scholar 

  8. M. Burkschat, E. Cramer, and U. Kamps, ‘‘Dual generalized order statistics,’’ Metron LXI (1), 13–26 (2003).

    MathSciNet  MATH  Google Scholar 

  9. I. Malinowska and D. Szynal, ‘‘On Characterization of Certain Distributions of \(k\)th Lower (Upper) Record Values,’’ Appl. Math. Comput. 202, 338–347 (2008).

    MathSciNet  MATH  Google Scholar 

  10. H. A. David and H. N. Nagaraja, Order Statistics (3rd ed., Wiley, New Jersey, 2003).

    Book  Google Scholar 

  11. T. S. Ferguson, ‘‘On characterizing distributions by properties of order statistics’’ Sankhyā, Ser. A 29, 265–278 (1967).

    MathSciNet  MATH  Google Scholar 

  12. U. Kamps, A Concept of generalized order statistics (Teubner, Stuttgart, 1995).

    Book  Google Scholar 

  13. C. Keseling, ‘‘Conditional distributions of generalized order statistics and some characterizations,’’ Metrika 49, 27–40 (1999).

    Article  MathSciNet  Google Scholar 

  14. A. H. Khan and M. S. Abu-Salih, ‘‘Characterizations of probability distributions by conditional expectations of order statistics,’’ Metron 47, 171–181 (1989).

    MathSciNet  MATH  Google Scholar 

  15. E. Cramer, U. Kamps, and C. Keseling, ‘‘Characterizations via linear regression of ordered random variables: a unifying approach,’’ Commun. Stat.-Theory Methods 33 (12), 2885–2911 (2004).

    Article  MathSciNet  Google Scholar 

  16. D. Pfeifer, ‘Record Values’ in einem stochastischen Modell mit nicht-identischen Verteilungen (Dissertation, Aachen University of Technology, 1979).

  17. D. Pfeifer, ‘‘Characterizations of exponential distributions by independent non-stationary record increments,’’ J. Appl. Probab., pp. 127–135; Correction: 19, 906 (1982).

    MATH  Google Scholar 

  18. P. Samuel, ‘‘Characterization of distributions by conditional expectation of generalized order statistics,’’ Stat. Pap., pp. 101–108 (2008).

  19. M. Tavangar and M. Asadi, ‘‘Some unified characterization results on the generalized pareto distributions based on generalized order statistics,’’ Metrika 75, 997–1007 (2012).

    Article  MathSciNet  Google Scholar 

  20. J. W. Wu and W. C. Lee ‘‘On the characterization of generalized extreme value, power function, generalized pareto and classical pareto distributions by conditional expectation of record values,’’ Stat. Pap. 42, 225–242 (2001).

    Article  MathSciNet  Google Scholar 

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ACKNOWLEDGMENTS

The authors would like to thank Associate Editor and two anonymous referees for their constructive comments and suggestions which improved the presentation of the paper.

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Correspondence to Mahdi Tavangar or Ismihan Bayramoglu.

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Tavangar, M., Bayramoglu, I. On Some Models of Ordered Random Variables and Characterizations of Distributions. Math. Meth. Stat. 29, 149–158 (2020). https://doi.org/10.3103/S1066530720030035

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