# Simulation from a conditional C- or D-vine Simulates from a d-dimensional conditional C- or D-vine of the variables (Y ,X ), given the fixed conditioning variables X . The algorithm works for vines satysfying the requirements discussed in **Bevacqua et al. (2017)**. The algorthm implemented here is a modified version of those form **Aas et al. (2009)** and is shown in **Bevacqua et al. (2017)**. ```r CDVineCondSim(RVM, Condition, N) ``` ## Arguments - `RVM`: An `RVineMatrix` object containing the information of the d-dimensional C- or D-Vine model (for further details about `RVineMatrix` objects see the documentation file of the `VineCopula` package). If the full copula is 2-dimensional, RVM can be an `RVineMatrix` object or a data.frame (or list) object where `$family`, `$par` and `$par2` are specified. - `Condition`: A `N x Nx` matrix of the Nx conditioning variables. For D-vine: data corresponding to the conditioning variable whose index is in `RVM$Matrix[i,i]`, are in i-th column of `Condition`. For C-vine: data corresponding to the conditioning variable whose index is in `RVM$Matrix[i,i]`, are in [(d+1)-i]-th column of `Condition`. See examples. - `N`: Number of data to be simulated. By default N is taken from `Condition`, which is a `N x Nx` matrix. It is necessary to specify `N` only when `Condition` is not given. ## Returns A `N x d` matrix of the simulated variables from the given C- or D-vine copula model. In the first columns there are the simulated conditioned variables, and in the last columns the conditioning variables `Condition`. For more details about the exact order of the variables in the columns see the examples. The function is built to work easily in combination with `CDVineCondFit`. ## Examples ```r # Example 1: conditional sampling from a C-Vine # Read data data(dataset) data <- dataset$data[1:400,1:4] # Define the variables Y and X. X are the conditioning variables, # which have to be positioned in the last columns of the data.frame colnames(data) <- c("Y1","Y2","X3","X4") ## Not run: # Select a vine and fit the copula families, specifying that there are 2 conditioning variables RVM <- CDVineCondFit(data,Nx=2,type="CVine") # Set the values of the conditioning variables as those used for the calibration. # Order them with respect to RVM$Matrix, considering that is a C-Vine d=dim(RVM$Matrix)[1] cond1 <- data[,RVM$Matrix[(d+1)-1,(d+1)-1]] cond2 <- data[,RVM$Matrix[(d+1)-2,(d+1)-2]] condition <- cbind(cond1,cond2) # Simulate the variables Sim <- CDVineCondSim(RVM,condition) # Plot the simulated variables over the observed Sim <- data.frame(Sim) overplot(Sim,data) # Example 2: conditional sampling from a D-Vine # Read data data(dataset) data <- dataset$data[1:100,1:4] # Define the variables Y and X. X are the conditioning variables, # which have to be positioned in the last columns of the data.frame colnames(data) <- c("Y1","Y2","X3","X4") # Select a vine and fit the copula families, specifying that there are 2 conditioning variables RVM <- CDVineCondFit(data,Nx=2,type="DVine") summary(RVM) #It is a D-Vine. # Set the values of the conditioning variables as those used for the calibration. # Order them with respect to RVM$Matrix, considering that is a D-Vine. cond1 <- data[,RVM$Matrix[1,1]] cond2 <- data[,RVM$Matrix[2,2]] condition <- cbind(cond1,cond2) # Simulate the variables Sim <- CDVineCondSim(RVM,condition) # Plot the simulated variables over the observed Sim <- data.frame(Sim) overplot(Sim,data) # Example 3 # Read data data(dataset) data <- dataset$data[1:100,1:2] colnames(data) <- c("Y1","X2") # Fit copula require(VineCopula) BiCop <- BiCopSelect(data$Y1,data$X2) BiCop # Fix conditioning variable to low values and simulate condition <- data$X2/10 Sim <- CDVineCondSim(BiCop,condition) # Plot the simulated variables over the observed Sim <- data.frame(Sim) overplot(Sim,data) ## End(Not run) ``` ## Author(s) Emanuele Bevacqua ## References Bevacqua, E., Maraun, D., Hobaek Haff, I., Widmann, M., and Vrac, M.: Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy), Hydrol. Earth Syst. Sci., 21, 2701-2723, https://doi.org/10.5194/hess-21-2701-2017, 2017. [[link]](https://www.researchgate.net/publication/317414374_Multivariate_statistical_modelling_of_compound_events_via_pair-copula_constructions_Analysis_of_floods_in_Ravenna_Italy) [[link]](https://www.hydrol-earth-syst-sci.net/21/2701/2017/hess-21-2701-2017.html) Aas, K., Czado, C., Frigessi, A. and Bakken, H.: Pair-copula constructions of multiple dependence, Insurance: Mathematics and Economics, 44(2), 182-198, , 2009. [[link]](http://www.sciencedirect.com/science/article/pii/S0167668707000194) Ulf Schepsmeier, Jakob Stoeber, Eike Christian Brechmann, Benedikt Graeler, Thomas Nagler and Tobias Erhardt (2017). VineCopula: Statistical Inference of Vine Copulas. R package version 2.1.1. [[link]](https://CRAN.R-project.org/package=VineCopula) ## See Also `CDVineCondFit`

CDVineCondSim function