Centers of probability measures without the mean

Giovanni Puccetti, Pietro Rigo, Bin Wang and Ruodu Wang
Additional contact information
Pietro Rigo: University of Pavia
Bin Wang: Chinese Academy of Sciences
Ruodu Wang: University of Waterloo

Journal of Theoretical Probability, 2019, vol. 32, issue 3, 1482-1501

Abstract: Abstract In the recent years, the notion of mixability has been developed with applications to operations research, optimal transportation, and quantitative finance. An n-tuple of distributions is said to be jointly mixable if there exist n random variables following these distributions and adding up to a constant, called center, with probability one. When the n distributions are identical, we speak of complete mixability. If each distribution has finite mean, the center is obviously the sum of the means. In this paper, we investigate the set of centers of completely and jointly mixable distributions not having a finite mean. In addition to several results, we show the (possibly counterintuitive) fact that, for each $$n \ge 2$$ n ≥ 2 , there exist n standard Cauchy random variables adding up to a constant C if and only if $$\begin{aligned} |C|\le \frac{n\,\log (n-1)}{\pi }. \end{aligned}$$ | C | ≤ n log ( n - 1 ) π .

Keywords: Cauchy distribution; Complete mixability; Joint mixability; Multivariate dependence; 60E05; 60E07 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-018-0815-3 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:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-018-0815-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-018-0815-3

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().