Previous |  Up |  Next

# Article

Full entry | PDF   (0.9 MB)
Keywords:
copula; noise; perturbation of copula; random vector
Summary:
For a random vector $(X,Y)$ characterized by a copula $C_{X,Y}$ we study its perturbation $C_{X+Z,Y}$ characterizing the random vector $(X+Z,Y)$ affected by a noise $Z$ independent of both $X$ and $Y$. Several examples are added, including a new comprehensive parametric copula family $\left(\mathcal{C}_k \right) _{k \in [-\infty, \infty]}$.
References:
[1] Cherubini, U., Gobbi, F., Mulinacci, S.: Convolution Copula Econometrics. Springer-Briefs in Statistics 2016. DOI 10.1007/978-3-319-48015-2 | MR 3586607
[2] Durante, F., Sempi, C.: Principles of Copula Theory. CRC Chapman and Hall, Boca Raton 2016. DOI 10.1201/b18674 | MR 3443023
[3] Gijbels, I., Herrmann, K.: On the distribution of sums of random variables with copula-induced dependence. Insurance Math. Econom. 59 (2014), C, 27-44. DOI 10.1016/j.insmatheco.2014.08.002 | MR 3283206
[4] Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall 1997. DOI 10.1201/b13150 | MR 1462613 | Zbl 0990.62517
[5] Nelsen, R. B.: An introduction to copulas. Second edition. Springer Series in Statistics, Springer-Verlag, New York 2006. DOI 10.1007/0-387-28678-0 | MR 2197664
[6] Sklar, A.: Fonctions de répartition a n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris \mi{8} (1959), 229-231. MR 0125600
[7] Wang, R.: Sum of arbitrarily dependent random variables. Electron. J. Probab. 19 (2014), 84, 1-18. DOI 10.1214/ejp.v19-3373 | MR 3263641
[8] Williamson, R. C., Downs, R. C.: Probabilistic arithmetic I: numerical methods for calculating convolutions and dependency bounds. Int. J. Approx. Reason. 4 (2014), 89-158. DOI 10.1016/0888-613x(90)90022-t | MR 1042207

Partner of