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Characterizations of discrete distributions based on conditional expectations of record values

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Abstract

In this paper we study the conditional expectation of r-th record values subject to (r + l)-th record values, record mean function, from a distribution of discrete type. We give some properties of the record mean function and an explicit expression for the distribution function based on its record mean function, which allows us to characterize particular discrete distributions using the record mean functions.

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References

  1. Ahsanullah, M. (1995). Record statistics. Ed. Nova Science Publishers, New York.

    MATH  Google Scholar 

  2. Ahsanullah, M. and Holland, B. (1984). Record values and the geometric distribution. Statistical Papers, 25, 319–327.

    MATH  MathSciNet  Google Scholar 

  3. Aliev, F.A. (1998). Characterization of distributions through weak records. J. Appl. Statist. Sci., 8, 13–16.

    MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  6. Dallas, A.C. (1989). Some properties of record values coming from the geometric distribution. Ann. Inst. Statist. Math., 41, 661–669.

    Article  MATH  MathSciNet  Google Scholar 

  7. Deheuvels, P. (1984). The characterization of distributions by order statistics and record values.- A unified approach. J. Appl. Prob., 21, 326–334.

    Article  MATH  MathSciNet  Google Scholar 

  8. Franco, M. and Ruiz, J.M. (1996). On characterizations of continuous distributions by conditional expectation of record values. Sankhya Ser. A, 58, 135–141.

    MATH  MathSciNet  Google Scholar 

  9. Glick, N. (1982). Breaking records and breaking boards. Amer. Math. Monthly, 85, 2–26.

    Article  MathSciNet  Google Scholar 

  10. Huang, W.J. and Li, S.H. (1993). Characterization results based on record values. Statistica Sinica, 3, 583–599.

    MATH  MathSciNet  Google Scholar 

  11. Kalbfleisch, J.D. and Prentice, R.L. (1980). The Statistical Analysis of Failure Time Data. Ed. J. Wiley, New York.

    MATH  Google Scholar 

  12. Korwar, R.M. (1984). On characterizing distributions for which the second record value has a linear on the first. Sankhya Ser. B, 46, 108–109.

    MathSciNet  Google Scholar 

  13. Mohan, N.R. and Nayak, S.S. (1982). A characterization based on the equidistribution of the first two spacings of record values. Z. Wahrscheinl. verw. Gebiete, 60, 219–221.

    Article  MATH  MathSciNet  Google Scholar 

  14. Nagaraja, H.N. (1988). Some characterizations of continuous distributions based on regressions of adjacent order statistics and record values. Sankhya Ser. A, 50, 70–73.

    MATH  MathSciNet  Google Scholar 

  15. Nagaraja, H.N., Sen, P. and Srivastava, R.C. (1989). Some characterizations of geometric tail distributions based on record values. Statistical Papers, 30, 147–155.

    Article  MATH  MathSciNet  Google Scholar 

  16. Nevzorov, V.B. (1987). Records. Theory Prob. Appl., 32, 201–228.

    Article  MATH  Google Scholar 

  17. Srivastava, R.C. (1979). Two characterizations of the geometric distribution by record values. Sankhyā Ser. B, 40, 276–278.

    MATH  Google Scholar 

  18. Srivastava, R.C. (1981). On some characterizations of the geometric distribution. In: C. Taulie et al. Eds., Statistical Distributions in Scientific Work, Vol. 4. D. Reidel Publishing Company, Dordrecht, 349–355.

    Google Scholar 

  19. Stepanov, A.B. (1990). Characterizations of a geometric class of distributions. Theor. Probab. Math. Statist., 41, 133–136.

    MATH  Google Scholar 

  20. Stepanov, A.B. (1994). A characterization theorem for weak records. Theory Prob. Appl., 38, 762–764.

    Article  Google Scholar 

  21. Vervaat, W. (1973). limit theorems for records from discrete distributions. Stochastic Process. Appl.

  22. Wesolowski, J. and Ahsanullah, M. (1999). Linearity of regression for nonadjacent weak records. To appear in Statistica Sinica.

  23. Witte, H.J. (1990). Characterizations of distributions of exponential or geometric type by the integrated lack of memory and record values. Comput. Statist. Data Anal., 10, 283–288.

    Article  MATH  MathSciNet  Google Scholar 

  24. Witte, H.J. (1993). Some characterizations of distributions of exponential or geometric distributions in a non-stationary record values model. J. Appl. Prob., 30, 373–381.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Departamento de Estadistica e I.O., Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain

    Manuel Franco & José M. Ruiz

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  1. Manuel Franco
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  2. José M. Ruiz
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Correspondence to Manuel Franco or José M. Ruiz.

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Supported by DGES of the MEC, under Grant PB96-1105.

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Franco, M., Ruiz, J.M. Characterizations of discrete distributions based on conditional expectations of record values. Statistical Papers 42, 101–110 (2001). https://doi.org/10.1007/s003620000043

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  • DOI: https://doi.org/10.1007/s003620000043

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