Description Usage Arguments Details Value Author(s) See Also Examples
Creates an instance of the multivariate asymmetric copula with parameters θ and r.
1 | NewMEVAsyLogisticCopula(theta, r)
|
theta |
a k x d matrix of reals. |
r |
a vector of k reals |
If theta
has entries θ_{ij} and r
has entries r_j (i=1,…,k and j=1,…,d), then the following parameterisation of the copula is used:
C(u_1,…,u_d) = exp(- ∑_i { ∑_j (θ_{ij} v_j)^{r_i} }^{1/r_i} )
where v_j = -log(u_j), j=1,…,d.
Necessary and sufficient conditions for the parameters are
all entries in theta
have to be non-negative.
each column of theta
has to add to one.
each row of theta
must have a unique pattern of non-zero values, including the pattern that has no zeros in a row.
if a row of theta
has only one non-zero value, then the corresponding entry in r
has to be one.
if a row of theta
has more than one non-zero value, then the corresponding entry of r
must be greater than one.
A function that evaluates the multivariate asymmetric logistic copula (with parameters θ and r) at a given d-dimensional vector in the unit square. Note that for this function the dimension of vectors at which the copula can be evaluated is determined by the input parameters. The environment of the function also contains a function called pdfCopula
that evaluates the probability density function of the multivariate asymmetric logistic copula via automatic differentation.
Berwin A. Turlach <berwin.turlach@gmail.com>
NewBEVAsyLogisticCopula
, NewMEVGumbelCopula
1 2 3 4 5 6 7 8 9 10 11 12 | theta <- rbind(c(0, 0.2, 0.8), c(1,0.8,0.2))
r <- c(2,3)
cop <- NewMEVAsyLogisticCopula(theta, r)
## Creates the same copula
theta <- 0.2
phi <- 0.4
r <- 2
cop1 <- NewBEVAsyLogisticCopula(r, theta, phi)
theta <- cbind(c(phi, 1-phi, 0), c(theta, 0, 1-theta))
r <- c(r, 1, 1)
cop2 <- NewMEVAsyLogisticCopula(theta, r)
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