Stochastic comparisons and bounds for conditional distributions by using copula properties. (English) Zbl 1404.62057
Summary: We prove that different conditional distributions can be represented as distorted distributions. These representations are used to obtain stochastic comparisons and bounds for them based on properties of the underlying copula. These properties can be used to explain the meaning of mathematical properties of copulas connecting them with dependence concepts. Some applications and illustrative examples are provided as well.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 60E15 | Inequalities; stochastic orderings |
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