Uniqueness of characterization of absolutely continuous distributions by regressions of generalized order statistics

Mariusz Bieniek () and Krystyna Macia̧g ()
Additional contact information
Mariusz Bieniek: Maria Curie Skłodowska University
Krystyna Macia̧g: Ernst and Young Ltd.

AStA Advances in Statistical Analysis, 2018, vol. 102, issue 3, No 3, 359-380

Abstract: Abstract We provide a new approach to the problem of the unique identification of distributions with a continuous density by a single regression function of order statistics or record values or, more generally, generalized order statistics. Using their Markov property we show that the characterization is unique if and only if the corresponding system of differential equations has the unique solution. This result is new even in the particular case of ordinary order statistics. This approach provides a new proof of characterization of power, exponential and Pareto distributions by linearity of corresponding regression. It also yields new examples of characterizations of distributions.

Keywords: Characterization; Generalized order statistics; Regression; Order statistics; Record values; 62G30; 62E10; 60E05 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10182-017-0310-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:alstar:v:102:y:2018:i:3:d:10.1007_s10182-017-0310-7

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10182/PS2

DOI: 10.1007/s10182-017-0310-7

Access Statistics for this article

AStA Advances in Statistical Analysis is currently edited by Göran Kauermann and Yarema Okhrin

More articles in AStA Advances in Statistical Analysis from Springer, German Statistical Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().