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Ahsanullah, M. , On characterizations of the uniform distribution based on functions of order statistics, Comm. Statist. Theory Methods , 33 (2004), no. 11–12, 2921–2928. Ahsanullah M

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The properties of the empirical density function,f n(x) = k/n(ξj + − ξj-1 +) ifξ j-1 + < x ≤ ξ+ whereξ j-1 + andξ j + are sample elements and there are exactlyk − 1 sample elements between them, are studied in that practical point of view how to choose a suitablek for a “good” estimation. A bound is given for the expected value of the absolute value of difference between the empirical and theoretical density functions.

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. , Records , John Wiley & Sons Inc , New York , 1998 . [4] Bairamov , I. and Bekci , M. , Concomitant of order statistics in FGM type

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] Hamedani , G. G. , Characterizations of continuous univariate distributions based on the truncated moments of functions of order statistics , Studia Sci. Math. Hungar. , 47 ( 2010 ), 462 – 484 . [39

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Scientometrics
Authors: A. I. Pudovkin and Eugene Garfield

are progressively higher in later years, which is probably due to the dramatic world-wide increase in the number of publications. This is an additional argument to use order statistics (e.g. percentile ranking; see above) in dealing with IFs

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Abstract  

We consider an empirical process based upon ratios of selected pairs of spacings, generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on (possibly shifted) intervals of equal lengths, this empirical process converges to a mean-centered Brownian bridge of the form B C(u) = B(u)−6Cu(1−u) Σ0 1 B(s)ds, where B(·) denotes a Brownian bridge, and C, a constant. The investigation of the class of Gaussian processes {B C(·): C ∈ ℝ} leads to some unexpected distributional identities such as B 2(·)

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B(·). We discuss this and similar results in an extended framework.

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Bieniek, M. and Szynal, D. , Characterizations of distributions via linearity of regression of generalized order statistics. Metrika , 58 (2007), 259–271. Szynal D

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