The new class of matrix-tilted Archimedean copulas is introduced. It combines properties and elliptical by introducing a tilting matrix in the stochastic representation copulas, similar to Cholesky factor for copulas. Basic this copula construction are discussed further extension outlined.

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization ...

The package copula (formerly nacopula) provides procedures for constructing nested Archimedean copulas in any dimensions and with any kind of nesting structure, generating vectors of random variates from the constructed objects, computing function values and probabilities of falling into hypercubes, as well as evaluation of characteristics such as Kendall’s tau and the tail-dependence coefficie...

Formulae for the distribution of the losses of a loan portfolio that are both realistic and simple enough to be implemented in a spreadsheet are hard to come by. The most prominent example is the Vasicek (1987) formula which is based upon a simplified version of the multivariate Merton (1974) model. Using an algorithm from the theory of Archimedean Copula functions, this paper gives some more l...

This work considers stochastic comparisons of lifetimes series and parallel systems with dependent heterogeneous components having following the proportional odds (PO) model. The joint distribution component is modeled by Archimedean survival copula. We discuss some potential applications our findings in system reliability actuarial science.