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#'@title Conditional distribution of non-central squared copula
#'
#'@description This function computes the conditional distribution of the non-central squared copula (ncs) associated with a one-parameter copula with parameter cpar, and parameters a1, a2 >0 .
#'@param data Matrix (x,y) of size n x 2
#'@param cond_var Conditioning variable (1 or 2)
#'@param family Copula family: "ncs-gaussian", "ncs-clayton", "ncs-frank", "ncs-gumbel", "ncs-joe", "ncs-plackett''.
#'@param rotation Rotation: 0 (default value), 90, 180, or 270.
#'@param par vector of copula parameter and non-centrality parameter a1,a2 >0
#'
#'
#'
#'@return \item{h}{Conditional cdf}
#'
#'@references Nasri (2020). On non-central squared copulas. Statistics and Probability Letters.
#'
#'@examples
#' hncs(c(0.5,0.8),1,"ncs-clayton",270,c(2,1,2))
#'
#'
#'@export
#'
#'
hncs=function(data, cond_var, family, rotation=0,par){
cpar1=c("ncs-gaussian", "ncs-clayton", "ncs-frank", "ncs-gumbel", "ncs-joe", "ncs-plackett")
if(family %in% cpar1)
{
if(is.vector(data)){data = matrix(data,ncol=2)}
u = data[,1]
v = data[,2]
if(rotation ==0){return(ccdf(u,v,cond_var,family,par))}
else if(rotation==90){
if(cond_var==2){ return(1-ccdf(1-u,v,2,family,par))}else{
return(ccdf(u,1-v,1,family,par))}}
else if(rotation==180){
return(1-ccdf(1-u,1-v,cond_var,family,par))}
else if(rotation==270){
if(cond_var==2){
return(ccdf(u,1-v,2,family,par))
}else{
return(1-ccdf(u,1-v,1,family,par))}
}
}else{warning("Family not available")
return(NULL)}
}
ccdf =function(u1,u2,cond_var,family,par){
family0=gsub('ncs-', '', family)
cpar=par[1]
a1 = par[2]
a2 = par[3]
d1 = a1^2;
d2 = a2^2;
G1 = sqrt(qchisq(u1,1,d1)) #Ga inverse
G2 = sqrt(qchisq(u2,1,d2))
ha = cbind((G1-a1), (-G1-a1) , (G2-a2) ,(-G2-a2))
htilde = pnorm(ha)+ 1E-10;
w0 = dnorm(ha);
U11 = cbind(htilde[,1], htilde[,3])
U12 = cbind(htilde[,1], htilde[,4])
U21 = cbind(htilde[,2], htilde[,3])
U22 = cbind(htilde[,2], htilde[,4])
w0011 = w0[,1] /(w0[,1]+w0[,2]);
w0012 = 1-w0011;
w0021 = w0[,3] /(w0[,3]+w0[,4]);
w0022 = 1-w0021;
if(family0=="plackett")
{
CCop = function(u) {hplac(u,cond_var,rotation=0,cpar);}
}else{
CCop = function(u) {rvinecopulib::hbicop(u,cond_var,family0,rotation=0,cpar);}
}
G11 = CCop(U11)
G12 = CCop(U12)
G21 = CCop(U21)
G22 = CCop(U22)
if(cond_var==1){
return(w0011 * (G11 - G12) + (1-w0011) * (G21-G22))}else{
return(w0021 * (G11 - G21) + (1-w0021) * (G12-G22))}
}
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