Functions operating on multivariate distribution and survival functions-With applications to classical mean-values and to copulas

JOURNAL OF MULTIVARIATE ANALYSIS

卷:105

Article

Ressel, Paul

关键词: Multivariate distribution function;    Multivariate survival function;    Fully n-increasing;    n-monotone;    n-absolutely monotone;    Copula;    Classical mean value;   

DOI  :  10.1016/j.jmva.2011.08.007

来源: Elsevier

【 摘 要 】

Functions operating on multivariate distribution and survival functions are characterized, based on a theorem of Morillas, for which a new proof is presented. These results are applied to determine those classical mean values on [0, 1](n) which are distribution functions of probability measures on [0, 1](n). As it turns out, the arithmetic mean plays a universal role for the characterization of distribution as well as survival functions. Another consequence is a far reaching generalization of Kimberling's theorem, tightly connected to Archimedean copulas. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free