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

Mahdi Tavangar () and Marzieh Hashemi ()

Statistical Papers, 2013, vol. 54, issue 2, 390 pages

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

Keywords: Exponential distribution; Functional equations; Quantile function; Residual lifetime; Censoring scheme (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00362-012-0434-5

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