Vine copula distributions

Density, distribution function and random generation for the vine copula distribution.

Usage

dvinecop(u, vinecop, cores = 1)

pvinecop(u, vinecop, n_mc = 10^4, cores = 1)

rvinecop(n, vinecop, qrng = FALSE, cores = 1)

Arguments

u: matrix of evaluation points; must contain at least d columns, where d is the number of variables in the vine. More columns are required for discrete models, see Details.
vinecop: an object of class "vinecop_dist".
cores: number of cores to use; if larger than one, computations are done in parallel on cores batches .
n_mc: number of samples used for quasi Monte Carlo integration.
n: number of observations.
qrng: if TRUE, generates quasi-random numbers using the multivariate Generalized Halton sequence up to dimension 300 and the Generalized Sobol sequence in higher dimensions (default qrng = FALSE).

Value

dvinecop() gives the density, pvinecop() gives the distribution function, and rvinecop() generates random deviates.

The length of the result is determined by n for rvinecop(), and the number of rows in u for the other functions.

The vinecop object is recycled to the length of the result.

Details

See vinecop() for the estimation and construction of vine copula models.

The copula density is defined as joint density divided by marginal densities, irrespective of variable types.

Discrete variables

When at least one variable is discrete, two types of "observations" are required in u: the first \(n \; x \; d\) block contains realizations of \(F_{X_j}(X_j)\). The second \(n \; x \; d\) block contains realizations of \(F_{X_j}(X_j^-)\). The minus indicates a left-sided limit of the cdf. For, e.g., an integer-valued variable, it holds \(F_{X_j}(X_j^-) = F_{X_j}(X_j - 1)\). For continuous variables the left limit and the cdf itself coincide. Respective columns can be omitted in the second block.

Examples

## simulate dummy data
x <- rnorm(30) * matrix(1, 30, 5) + 0.5 * matrix(rnorm(30 * 5), 30, 5)
u <- pseudo_obs(x)

## fit a model
vc <- vinecop(u, family = "clayton")

# simulate from the model
u <- rvinecop(100, vc)
pairs(u)


# evaluate the density and cdf
dvinecop(u[1, ], vc)
#> [1] 104.7548
pvinecop(u[1, ], vc)
#> [1] 0.6646

## Discrete models
vc$var_types <- rep("d", 5)  # convert model to discrete

# with discrete data we need two types of observations (see Details)
x <- qpois(u, 1)  # transform to Poisson margins
u_disc <- cbind(ppois(x, 1), ppois(x - 1, 1))

dvinecop(u_disc[1:5, ], vc)
#> [1] 46.60577506  3.40840087  2.14675926  0.05626392  2.16598614
pvinecop(u_disc[1:5, ], vc)
#> [1] 0.7886 0.2459 0.5223 0.2432 0.2142

# simulated data always has uniform margins
pairs(rvinecop(200, vc))