CDF of an R-Vine Copula Model

This function calculates the cumulative distribution function of a d-dimensional R-vine copula.

RVineCDF(data, RVM, N = 1000)

Arguments

data

An N x d data matrix that specifies where the CDF shall be evaluated.

RVM

An RVineMatrix() object including the structure and the pair-copula families and parameters.

N

Number of points to simulate for the Monte Carlo integration (default: n = 1000).

Value

A vector of length N with the CDF values.

Details

The cumulative distribution function of a \(d\)-dimensional R-vine copula cannot be expressed in closed form. However, it can be calculated by numerical integration. The function uses the RVineSim() function to simulate a grid of points and then computes the CDF via Monte Carlo.

See also

RVineSim(), RVineMatrix(), RVineLogLik(), RVinePDF()

Author

Thibault Vatter

Examples

# define 5-dimensional R-vine tree structure matrix
Matrix <- c(
  5, 2, 3, 1, 4,
  0, 2, 3, 4, 1,
  0, 0, 3, 4, 1,
  0, 0, 0, 4, 1,
  0, 0, 0, 0, 1
)
Matrix <- matrix(Matrix, 5, 5)

# define R-vine pair-copula family matrix
family <- c(
  0, 1, 3, 4, 4,
  0, 0, 3, 4, 1,
  0, 0, 0, 4, 1,
  0, 0, 0, 0, 3,
  0, 0, 0, 0, 0
)
family <- matrix(family, 5, 5)

# define R-vine pair-copula parameter matrix
par <- c(
  0, 0.2, 0.9, 1.5, 3.9,
  0, 0, 1.1, 1.6, 0.9,
  0, 0, 0, 1.9, 0.5,
  0, 0, 0, 0, 4.8,
  0, 0, 0, 0, 0
)
par <- matrix(par, 5, 5)

# define second R-vine pair-copula parameter matrix
par2 <- matrix(0, 5, 5)

# define RVineMatrix object
RVM <- RVineMatrix(
  Matrix = Matrix, family = family,
  par = par, par2 = par2,
  names = c("V1", "V2", "V3", "V4", "V5")
)

# compute the CDF at (0.1, 0.2, 0.3, 0.4, 0.5)
RVineCDF(c(0.1, 0.2, 0.3, 0.4, 0.5), RVM)
#> [1] 0.064