vines (version 1.0.1)

vinePIT-methods: Vine Probability Integral Transform Methods

Description

Probability integral transform (PIT) of (Rosenblatt, 1952) for vine models. The PIT converts a set of dependent variables into a new set of variables which are independent and uniformly distributed in $(0,1)$ under the hypothesis that the data follows a given multivariate distribution.

Usage

vinePIT(vine, u)

Arguments

vine

A Vine object.

u

Vector with one component for each variable of the vine or a matrix with one column for each variable of the vine.

Value

• A matrix with one column for each variable of the vine and one row for each observation.

References

Aas, K. and Czado, C. and Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44, 182--198.

Rosenblatt, M. (1952) Remarks on multivariate transformation. Annals of Mathematical Statistics 23, 1052--1057.

See Also

vinePIT.

Examples

dimension <- 3
copulas <- matrix(list(normalCopula(0.5), 
                       claytonCopula(2.75),
                       NULL, NULL),
                  ncol = dimension - 1,
                  nrow = dimension - 1,
                  byrow = TRUE)
vine <- CVine(dimension = dimension, trees = 1,
              copulas = copulas)

data <- matrix(runif(dimension * 100), 
               ncol = dimension, nrow = 100)

vinePIT(vine, data)