Sklar's Theorem in an Imprecise Setting
arXiv:1601.02121 · doi:10.1016/j.fss.2014.10.007
Abstract
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision.
A definitive version has been published in a special issue on uncertainty and imprecision modelling in decision making (EUROFUSE 2013) of Fuzzy Sets and Systems
Cited by in corpus (12)
- Final solution to the problem of relating a true copula to an imprecise copula
- Some multivariate imprecise shock model copulas
- Extreme semilinear copulas
- Correlated Boolean Operators for Uncertainty Logic
- Quasi-copulas as linear combinations of copulas
- Coherence and avoidance of sure loss for standardized functions and semicopulas
- On the quantification and efficient propagation of imprecise probabilities with copula dependence
- A complete characterization of normal cones and extreme points for -boxes
- Extending multivariate sub-quasi-copulas
- Relation between Blomqvist's beta and other measures of concordance of copulas
- A full scale Sklar's theorem in the imprecise setting
- Constructing copulas from shock models with imprecise distributions