prob {copula}

Computing Probabilities of Hypercubes

Description

Compute probabilities of a d-dimensional random vector U distributed according to a given copula x to fall in a hypercube (l,u], where l and u denote the lower and upper corners of the hypercube, respectively.

Usage

prob(x, l, u)

Arguments

x

copula of dimension d, that is, an object inheriting from Copula.

l, u

d-dimensional, numeric, lower and upper hypercube boundaries, respectively, satisfying 0 \le l_i \le u_i \le 1, for i\in{1,\dots,d}.

Value

A numeric in [0,1] which is the probability P(l_i< U_i \le u_i).

See Also

pCopula(.).

Examples

## Construct a three-dimensional nested Joe copula with parameters
## chosen such that the Kendall's tau of the respective bivariate margins
## are 0.2 and 0.5.
theta0 <- copJoe@iTau(.2)
theta1 <- copJoe@iTau(.5)
C3 <- onacopula("J", C(theta0, 1, C(theta1, c(2,3))))

## Compute the probability of a random vector distributed according to
## this copula to fall inside the cube with lower point l and upper
## point u.
l <- c(.7,.8,.6)
u <- c(1,1,1)
prob(C3, l, u)

## ditto for a bivariate normal copula with rho = 0.8 :
prob(normalCopula(0.8), c(.2,.4), c(.3,.6))