Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes

Foschi Rachele (), Nappo Giovanna () and Spizzichino Fabio L. ()
Additional contact information
Foschi Rachele: University of Pisa, Department of Economics and Management, Via C. Ridolfi, 10, 56124 Pisa, Italy
Nappo Giovanna: University of Rome La Sapienza, Department of Mathematics, Piazzale Aldo Moro, 5, 00185, Rome, Italy
Spizzichino Fabio L.: University of Rome La Sapienza, Piazzale Aldo Moro, 5, 00185, Rome, Italy

Dependence Modeling, 2021, vol. 9, issue 1, 394-423

Abstract: As a motivating problem, we aim to study some special aspects of the marginal distributions of the order statistics for exchangeable and (more generally) for minimally stable non-negative random variables T1, ..., Tr. In any case, we assume that T1, ..., Tr are identically distributed, with a common survival function ̄G and their survival copula is denoted by K. The diagonal sections of K, along with ̄G, are possible tools to describe the information needed to recover the laws of order statistics. When attention is restricted to the absolutely continuous case, such a joint distribution can be described in terms of the associated multivariate conditional hazard rate (m.c.h.r.) functions. We then study the distributions of the order statistics of T1, ..., Tr also in terms of the system of the m.c.h.r. functions. We compare and, in a sense, we combine the two different approaches in order to obtain different detailed formulas and to analyze some probabilistic aspects for the distributions of interest. This study also leads us to compare the two cases of exchangeable and minimally stable variables both in terms of copulas and of m.c.h.r. functions. The paper concludes with the analysis of two remarkable special cases of stochastic dependence, namely Archimedean copulas and load sharing models. This analysis will allow us to provide some illustrative examples, and some discussion about peculiar aspects of our results.

Keywords: Minimally stable random vectors; diagonal sections of survival copulas; diagonal dependence; t-exchangeability; absolute continuity; Archimedean copulas; load-sharing models (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/demo-2021-0119 (text/html)

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:vrs:demode:v:9:y:2021:i:1:p:394-423:n:16

DOI: 10.1515/demo-2021-0119

Access Statistics for this article

Dependence Modeling is currently edited by Giovanni Puccetti

More articles in Dependence Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().