Computing Probabilities of Hypercubes
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.
prob(x, l, u)
A numeric
in [0,1] which is the probability
P(l[i] < U[i] <= u[i]).
pCopula(.)
.
## 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))
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