Characterizations of the normal distribution via the independence of the sample mean and the feasible definite statistics with ordered arguments

Chin-Yuan Hu () and Gwo Dong Lin ()
Additional contact information
Chin-Yuan Hu: National Changhua University of Education
Gwo Dong Lin: Hwa-Kang Xing-Ye Foundation

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 3, No 4, 473-488

Abstract: Abstract It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov’s theorem, we further investigate the analogous characteristic properties in terms of the sample mean and some feasible definite statistics. The latter statistics introduced in this paper for the first time are based on nonnegative, definite and continuous functions of ordered arguments with positive degree of homogeneity. The proposed approach seems to be natural and can be used to derive easily characterization results for many feasible definite statistics, such as known characterizations involving the sample variance, sample range as well as Gini’s mean difference.

Keywords: Characterization of distributions; Order statistics; Anosov’s theorem; Benedetti’s inequality; Sample mean; Sample variance; Sample range; Gini’s mean difference (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10463-021-00805-3 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:aistmt:v:74:y:2022:i:3:d:10.1007_s10463-021-00805-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-021-00805-3

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().