 Characterizations based on the numbers of near-order statisticsM. Akbari, M. Fashandi () and Jafar Ahmadi () Statistical Papers, 2016, vol. 57, issue 1, 30 pages Abstract: In the present work, some characterization results are established based on the number of observations near the order statistics. Under some conditions, it is shown that the parent distribution can be uniquely determined by the moments of the number of observations in a random sample that fall within a left-hand or right-hand neighborhood of a specific order statistic. It is proved that the underlying distribution $$F$$ F belongs to the class of symmetric distributions if and only if the first moment of the number of observations in the right neighborhood of the $$k$$ k th order statistic and in the left neighborhood of the $$(n-k+1)$$ ( n - k + 1 ) th order statistic from a sample of size $$n$$ n are equal. Also, characterizations of the exponential distribution are presented. Copyright Springer-Verlag Berlin Heidelberg 2016 Keywords: Completeness properties; Exponential distribution; Müntz Theorem; Order statistics; Symmetric distribution; 62E10; 62G30; 60E10 (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:57:y:2016:i:1:p:21-30 Ordering information: This journal article can be ordered from DOI: 10.1007/s00362-014-0636-0 Access Statistics for this article Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller More articles in Statistical Papers from Springer |
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