Nothing
dmvEST = function(x,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,tau=0,nu){
#Validating Lambda
if(is.null(lambda)){
#not provided by user
stop("Skewness parameter 'lambda' must be provided (zero vector fot the symmetric case).")
}else{
#validate input
if(length(c(lambda)) != length(c(mu)) | !is.numeric(lambda)){
stop("Lambda must be numeric and have same dimension than mu.")
}
if(all(lambda==0)){
warning("Lambda = 0, t case is considered.",immediate. = TRUE)
return(dmvt(x = x,delta = c(mu),sigma = as.matrix(Sigma),df = nu,type = "shifted",log = FALSE))
}
}
if(is.null(tau)){
#not provided by user
stop("Extension parameter 'tau' must be provided for the EST case (zero for the Skew-t case).")
}else{
#validate input
if(!is.numeric(tau) | length(tau)>1){
stop("Tau must be numeric real number.")
}
tautil = tau/sqrt(1+sum(lambda^2))
if(pt(tautil,nu)< pnorm(-37)){
Delta = sqrtm(Sigma)%*%lambda/sqrt(1+sum(lambda^2))
Gamma = Sigma - Delta%*%t(Delta)
rownames(Gamma) <- colnames(Gamma)
omega_tau = (nu+tautil^2)/(nu+1)
return(dmvt(x = x,delta = c(mu - tautil*Delta),sigma = omega_tau*Gamma,df = nu+1,type = "shifted",log = FALSE))
}
return(dmvEST0(x,mu,Sigma,lambda,tau,nu))
}
}
########################################################################################################################
########################################################################################################################
dmvEST0 <- function(y, mu, Sigma, lambda,tau,nu){
#y: deve ser uma matrix onde cada linha tem um vetor de dados multivariados de dimens?o ncol(y) = p. nrow(y) = tamanho da amostra
#mu, lambda: devem ser do tipo vetor de mesma dimens?o igual a ncol(y) = p
#Sigma: Matrix p x p
if(length(c(mu)) == 1){return(dmvEST1(c(y),mu,Sigma,lambda,tau,nu))}
if(!is.matrix(y)){
y = matrix(y,ncol = nrow(Sigma),byrow = TRUE)
}
n <- nrow(y)
p <- ncol(y)
tautil<-tau/sqrt(1+sum(lambda^2))
nu2y = (nu + p)/(nu + mahalanobis(y,center = mu,cov = Sigma))
dens <- dmvt(x = y,delta = c(mu),sigma = Sigma,df = nu,type = "shifted",log = FALSE)*exp(
pt(sqrt(nu2y)*(
apply(matrix(rep(t(lambda)%*%solve(sqrtm(Sigma)),n), n, p, byrow = TRUE)*
(y - matrix(rep(mu, n), n, p, byrow = TRUE)), 1,sum) + tau),
df = nu+p,log.p = TRUE) - pt(tautil,nu,log.p = TRUE))
return(dens)
}
########################################################################################################################
########################################################################################################################
dmvEST1 <- function(y, mu=0, Sigma=1, lambda,tau,nu){
#y: deve ser uma matrix onde cada linha tem um vetor de dados multivariados de dimens?o ncol(y) = p. nrow(y) = tamanho da amostra
#mu, lambda: devem ser do tipo vetor de mesma dimens?o igual a ncol(y) = p
#Sigma: Matrix p x p
n <- length(c(y))
p <- 1
s = sqrt(Sigma)
tautil = tau/sqrt(1+sum(lambda^2))
if(pt(tautil,nu)< pnorm(-35)){
#print("normal aproximation")
Gamma = Sigma/(1+lambda^2)
mub = lambda*tau*Gamma/s
omega_tau = (nu+tautil^2)/(nu+1)
return(dent(y,mu-mub,omega_tau*Gamma,nu+1))
}
nu2y = (nu + 1)/(nu + ((y - mu)/s)^2)
dens <- dent(x = c(y),mu = c(mu),sigma2 = Sigma,nu = nu)*exp(
pt(q = sqrt(nu2y)*lambda*(y-mu)/s + tau,df = nu+1,log.p = TRUE) -
pt(tautil,nu,log.p = TRUE))
# pt(
# sqrt(nu2y)*(
# apply(matrix(rep(t(lambda)%*%solve(sqrtm(Sigma)),n), n, p, byrow = TRUE)*
# (y - matrix(rep(mu, n), n, p, byrow = TRUE)), 1,sum) + tau),
# df = nu+1,log.p = TRUE)
#
return(dens)
}
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