Liouville_marginal | R Documentation |
Marginal density, distribution, survival and inverse survival functions for Liouville copulas or Liouville vectors.
The inverse survival function of Liouville vectors is not available in closed-form and is obtained numerically by root-finding.
As such, Monte-Carlo approximation have been considered for dealing with inference to avoid computational bottlenecks.
Note: the arguments of sliouv
are reversed since they are meant to be called inside optim
. The functions borrow
psi functions and their derivatives from the copula-package
.
sliouvm(x, family, alpha, theta) pliouvm(x, family, alpha, theta) isliouvm(u, family, alpha, theta) dliouvm(x, family, alpha, theta)
x |
vector of quantiles from a Liouville copula (or a Liouville vector for the survival function , with support on the positive real line) |
family |
family of the Liouville copula. Either |
alpha |
integer Dirichlet parameter |
theta |
parameter of the corresponding Archimedean copula |
u |
vector of quantiles or survival probabilities, (pseudo)-uniform variates |
a vector with the corresponding quantile, probability, survival probabilities
## Not run: #Marginal density samp <- rliouv(n = 100, family = "clayton", alphavec <- c(2,3), theta = 2) dliouvm(x=samp[,1], family="clayton", alpha=2, theta=2) sum(log(dliouvm(x=samp[,1], family="clayton", alpha=2, theta=2))) #Marginal distribution and (inverse) survival function x <- rliouv(n = 100, family = "gumbel", alphavec <- c(2,3), theta = 2) pliouvm(x[,1], family="gumbel", alpha=alphavec[1], theta=2) su <- sliouvm(1-x[,1], family="gumbel", alpha=alphavec[1], theta=2) isliouvm(u=su, family="clayton", alpha=2, theta=2) #pliouv is the same as sliouv(isliouvm) ## End(Not run)
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