Centers of probability measures without the mean

doi:10.1007/s10959-018-0815-3

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	Centers of probability measures without the mean
	Puccetti, Giovanni 1; Rigo, Pietro 2; Wang, Bin3 ; Wang, Ruodu 4
	2019-09-01
发表期刊	JOURNAL OF THEORETICAL PROBABILITY
ISSN	0894-9840
卷号	32 期号:3 页码:1482-1501
摘要	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 >= 2, there exist n standard Cauchy random variables adding up to a constant C if and only if vertical bar C vertical bar <= n log (n - 1)/pi .
关键词	Cauchy distribution Complete mixability Joint mixability Multivariate dependence
DOI	10.1007/s10959-018-0815-3
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000476509700016
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35278
专题	应用数学研究所
通讯作者	Puccetti, Giovanni
作者单位	1.Univ Milan, Dept Econ Management & Quantitat Methods, Milan, Italy 2.Univ Pavia, Dept Math, Pavia, Italy 3.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Random Complex Struct & Data Sci, Beijing, Peoples R China 4.Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON, Canada
推荐引用方式 GB/T 7714	Puccetti, Giovanni,Rigo, Pietro,Wang, Bin,et al. Centers of probability measures without the mean[J]. JOURNAL OF THEORETICAL PROBABILITY,2019,32(3):1482-1501.
APA	Puccetti, Giovanni,Rigo, Pietro,Wang, Bin,&Wang, Ruodu.(2019).Centers of probability measures without the mean.JOURNAL OF THEORETICAL PROBABILITY,32(3),1482-1501.
MLA	Puccetti, Giovanni,et al."Centers of probability measures without the mean".JOURNAL OF THEORETICAL PROBABILITY 32.3(2019):1482-1501.