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On characterizations of the generalized Pareto distributions based on progressively censored order statistics

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Abstract

It is well-known, in the literature, that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. In the present paper, we consider the functional equation

$$F(x) = F(xy) + F(xQ(y)), \quad x, xQ(y) \in [0, \theta),\; y \in [0,1],$$

where F and Q satisfy certain conditions, to give some new characterization results on the generalized Pareto distributions based on progressively Type-II right censored order statistics. We prove the main results without restricting to distributions that are absolutely continuous with respect to Lebesgue measure.

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References

  • Aczel J, Ger R, Jarai A (1999) Solution of a functional equation arising from utility that is both separable and additive. Proc Am Math Soc 127: 2923–2929

    Article  MathSciNet  MATH  Google Scholar 

  • Asadi M, Rao CR, Shanbhag DN (2001) Some unified characterization results on the generalized Pareto distribution. J Stat Plan Inference 93: 29–50

    Article  MathSciNet  MATH  Google Scholar 

  • Azlarov TA, Volodin NA (1986) Characterization problems associated with the exponential distribution. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  • Bairamov I, T (2007) On characterization of distributions through the properties of conditional expectations of order statistics. Commun Stat Theory Methods 36: 1319–1326

    Article  MATH  Google Scholar 

  • Balakrishnan N, Aggarwala R (2000) Progressive censoring: theory, methods and application. Birkhäuser Publishers, Boston

    Book  Google Scholar 

  • Balakrishnan N, Dembińska A (2008a) Progressively type-II right censored order statistics from discrete distributions. J Stat Plan Inference 138: 845–856

    Article  MATH  Google Scholar 

  • Balakrishnan N, Dembińska A (2008b) Erratum to “Progressively Type-II right censored order statistics from discrete distributions” [J Stat Plan Inference 138 (2008), 845–856]. J Stat Plan Inference 139: 1572–1574

    Article  Google Scholar 

  • Ferguson TS (1967) On characterizing distributions by properties of order statistics. SankhyāA 29: 265–278

    MathSciNet  MATH  Google Scholar 

  • Galambos J, Kotz S (1978) Characterization of probability distributions. Lecture notes in mathematics, vol 675. Springer, Berlin

    Google Scholar 

  • Hall WJ, Wellner JA (1981) Mean residual life. In: Csorgo M, Dawson DA, Rao JNK, Md. Saleh E (eds) Statistics and related topics. North-Holland, Amsterdam, pp 169–184

    Google Scholar 

  • Hashemi M, Asadi M (2007) Some characterization results on generalized Pareto distribution based on progressive type-II right censoring. J Iran Stat Soc 6(2): 99–110

    MathSciNet  Google Scholar 

  • Hashemi M, Tavangar M, Asadi M (2010) Some properties of the residual lifetime of progressively type-II right censored order statistics. Stat Probab Lett 80: 845–859

    Article  MathSciNet  Google Scholar 

  • Marsaglia G, Tubilla A (1975) A note on the “lack of memory” property of the exponential distribution. Ann Probab 3(2): 353–354

    Article  MathSciNet  MATH  Google Scholar 

  • Nagaraja HN (1977) On a characterization based on record values. Aust J Stat 19: 70–73

    Article  MathSciNet  MATH  Google Scholar 

  • Oakes D, Dasu T (1990) A note on residual life. Biometrika 77: 409–410

    Article  MathSciNet  MATH  Google Scholar 

  • Rao CR, Shanbhag DN (1986) Recent results on characterization of probability distributions: a unified approach through extensions of Deny’s theorem. Adv Appl Probab 18: 660–678

    Article  MathSciNet  MATH  Google Scholar 

  • Rao CR, Shanbhag DN (1994) Choquet-Deny type functional equations with applications to stochastic models. Wiley, Chichester

    MATH  Google Scholar 

  • Ravi S (2010) On a characteristic property of generalized Pareto distributions, extreme value distributions and their max domain of attraction. Stat Papers 51(2): 455–463

    Article  MathSciNet  MATH  Google Scholar 

  • Resnick SI (2001) A probability path. Birkhäuser, Boston

    Google Scholar 

  • Tavangar M, Asadi M (2007) Generalized Pareto distributions characterized by generalized order statistics. Commun Stat Theory Methods 36(7): 1333–1341

    Article  MathSciNet  MATH  Google Scholar 

  • Tavangar M, Asadi M (2008) On a characterization of generalized Pareto distribution based on generalized order statistics. Commun Stat Theory Methods 37(9): 1347–1352

    Article  MathSciNet  MATH  Google Scholar 

  • Tavangar M, Asadi M (2010) Some new characterization results on exponential and related distributions. Bull Iran Math Soc 36(1): 257–272

    MathSciNet  MATH  Google Scholar 

  • Wu JW, Lee WC (2001) On the characterization of generalized extreme value, power function, generalized Pareto and classical Pareto distributions by conditional expectation of record values. Stat Papers 42: 225–242

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Isfahan, Isfahan, Iran

    Mahdi Tavangar

  2. Faculty of Sciences, Najafabad Branch, Islamic Azad University, Isfahan, Iran

    Marzieh Hashemi

Authors
  1. Mahdi Tavangar
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  2. Marzieh Hashemi
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Correspondence to Mahdi Tavangar.

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Tavangar, M., Hashemi, M. On characterizations of the generalized Pareto distributions based on progressively censored order statistics. Stat Papers 54, 381–390 (2013). https://doi.org/10.1007/s00362-012-0434-5

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  • DOI: https://doi.org/10.1007/s00362-012-0434-5

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