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

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  • Mahdi Tavangar
  • Marzieh Hashemi

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Mahdi Tavangar & Marzieh Hashemi, 2013. "On characterizations of the generalized Pareto distributions based on progressively censored order statistics," Statistical Papers, Springer, vol. 54(2), pages 381-390, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:381-390
    DOI: 10.1007/s00362-012-0434-5
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    References listed on IDEAS

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    1. Hashemi, Marzieh & Tavangar, Mahdi & Asadi, Majid, 2010. "Some properties of the residual lifetime of progressively Type-II right censored order statistics," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 848-859, May.
    2. Jong-Wuu Wu & Wen-Chuan Lee, 2001. "On the characterization of generalized extreme value, power function, generalized Pareto and classical Pareto distributions by conditional expectation of record values," Statistical Papers, Springer, vol. 42(2), pages 225-242, April.
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    Cited by:

    1. Yuebao Wang & Hui Xu & Dongya Cheng & Changjun Yu, 2018. "The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands," Statistical Papers, Springer, vol. 59(1), pages 99-126, March.
    2. Tavangar, Mahdi & Bairamov, Ismihan, 2015. "On conditional residual lifetime and conditional inactivity time of k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 225-233.
    3. Shah, Imtiyaz A. & Barakat, H.M. & Khan, A.H., 2020. "Characterizations through generalized and dual generalized order statistics, with an application to statistical prediction problem," Statistics & Probability Letters, Elsevier, vol. 163(C).

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