vines (version 1.1.5)

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.

Methods

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)