# install.packages("name.package")
library(copula)
library(mnormt)
library(lattice)
library(mvtnorm)
library(VGAM)

# simulation from copula models

# independence copula
ic<-indepCopula(dim=2) 
wireframe2(ic, FUN=pCopula)
contourplot2(ic, FUN=pCopula)
set.seed(332)
n<-1000
U<-rCopula(n, copula=ic)
str(U)  # matrix nxd
plot(U, xlab=quote(U[1]), ylab=quote(U[2]), col=3)

# normal copula 
d<-2
set.seed(332)
rho<-0.7 #linear correlation
P<-matrix(rho, nrow=d, ncol=d)
diag(P)<-1
n<-1000
X<-rmvnorm(n, sigma=P)
plot(X, xlim=c(-4,4), ylim=c(-4,4), 
     xlab=quote(X[1]), ylab=quote(X[2]))
# PIT
U<-pnorm(X) # sample from normal copula with N(0,1) margins
plot(U)

## same as
set.seed(332)
U.<-rCopula(n, normalCopula(rho, dim=2))
plot(U., xlab=quote(U[1]), ylab=quote(U[2]))

# exponential margins Exp(2)
Y<-qexp(U, 2)
plot(Y, xlim=c(0,4), ylim=c(0,4), 
     xlab=quote(Y[1]), ylab=quote(Y[2]))

# pseudo-copula observations 
# rescaled ranks (empirical cdf's)
V<-pobs(Y)
plot(V, col=4, main="pseudo-copula observations")

# sampling from a Clayton and a survival Clayton copula 
cop<-claytonCopula(param = 2) 
U<-rCopula(n, copula=cop)
plot(U, xlab=quote(U[1]), ylab=quote(U[2]))
# survival Clayton Copula
V<-1-U
plot(V, xlab=quote(V[1]), ylab=quote(V[2]))

# sampling from t copula with fixed df 
# and inversion of Kendall's tau
nu<-4
param<-iTau(tCopula(df=nu), tau = 0.6)
tc<-tCopula(param, df=nu)
tc
set.seed(271)
U<-rCopula(n, copula=tc)
plot(U, col=6)
cor(U, method = "kendall")

#########################

data(loss)
?loss
#View(loss)
# loss: claims
# alae: expenses

LOSS<-loss$loss
ALAE<-loss$alae
plot(LOSS, ALAE, cex=0.5)
plot(log(LOSS), log(ALAE), cex=0.5)
#hist(LOSS, breaks=30)

Z<-pobs(cbind(LOSS, ALAE))
plot(Z)