For a random vector (X,Y) characterized by a copula CX,Y we study its perturbation CX+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 (Ck)k∈[−∞,∞].
We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the ∗-product and the ⋆-product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.
In the paper we investigate properties of maximum pseudo-likelihood estimators for the copula density and minimum distance estimators for the copula. We derive statements on the consistency and the asymptotic normality of the estimators for the parameters.
River runoff and sediment transport are two related random hydrologic variables. The traditional statistical analysis method usually requires those two variables to be linearly correlated, and also have an identical marginal distribution. Therefore, it is difficult to know exactly the characteristics of the runoff and sediment in reality. For this reason, copulas are applied to construct the joint probability distribution of runoff and sediment in this article. The risk of synchronous-asynchronous encounter probability of annual rich-poor runoff and sediment is also studied. At last, the characteristics of annual runoff and sediment with multi-time scales in its joint probability distribution space are simulated by empirical mode decomposition method. The results show that the copula function can simulate the joint probability distribution of runoff and sediment of Huaxia hydrological station in Weihe River well, and that such joint probability distribution has very complex change characteristics at time scales.