R/copgHsCond.r

In GJRM: Generalised Joint Regression Modelling

copgHsCond <- function(p1, p2, teta, dof = 3, BivD, min.pr, max.pr){



########################################################################################
# Rotations
########################################################################################

if(BivD %in% c("C90","J90","G90","GAL90") ) {
p1 <- 1 - p1 
teta <- -teta
}  

if(BivD %in% c("C180","J180","G180","GAL180") ) {
p1 <- 1 - p1
p2 <- 1 - p2
}  

if(BivD %in% c("C270","J270","G270","GAL270") ) {
p2 <- 1 - p2 
teta <- -teta 
}   
   
########################################################################################   
########################################################################################


if(BivD=="HO"){


c.copula.be1 <- (-log(p1))^(1/teta - 1) * ((-log(p1))^(1/teta) + (-log(p2))^(1/teta))^(teta - 
    1) * exp(-((-log(p1))^(1/teta) + (-log(p2))^(1/teta))^teta)/p1 

c.copula.be2 <- (-log(p2))^(1/teta - 1) * ((-log(p1))^(1/teta) + (-log(p2))^(1/teta))^(teta - 
    1) * exp(-((-log(p1))^(1/teta) + (-log(p2))^(1/teta))^teta)/p2 
  

}



if(BivD=="PL"){

c.copula.be1 <- (teta - (0.5 * ((2 * ((p1 + p2) * (teta - 1) + 1) - 4 * (p2 * 
    teta)) * (teta - 1)/sqrt(((p1 + p2) * (teta - 1) + 1)^2 - 
    4 * (p1 * p2 * teta * (teta - 1)))) + 1))/(2 * (teta - 1)) 

c.copula.be2 <- (teta - (0.5 * ((2 * ((p1 + p2) * (teta - 1) + 1) - 4 * (p1 * 
    teta)) * (teta - 1)/sqrt(((p1 + p2) * (teta - 1) + 1)^2 - 
    4 * (p1 * p2 * teta * (teta - 1)))) + 1))/(2 * (teta - 1)) 
  
  
}




if(BivD=="N"){


c.copula.be1 <- pnorm( (qnorm(p2) - teta*qnorm(p1))/sqrt(1 - teta^2)   )                            
c.copula.be2 <- pnorm( (qnorm(p1) - teta*qnorm(p2))/sqrt(1 - teta^2)   )  



}


if(BivD=="T"){
 

c.copula.be1 <- BiCopHfunc1(p1, p2, family = 2, par = teta, par2 = dof)                         
c.copula.be2 <- BiCopHfunc2(p1, p2, family = 2, par = teta, par2 = dof) 


}








if(BivD=="F"){

  c.copula.be1 <- (exp(teta)* (-1 + exp(p2* teta)))/(-exp((p1 + p2)* teta) + exp(teta)* (-1 + exp(p1* teta) + exp(p2* teta)))

  c.copula.be2 <- (exp(teta)* (-1 + exp(p1* teta)))/(-exp((p1 + p2)* teta) + exp(teta)* (-1 + exp(p2* teta) + exp(p1* teta)))

}





if(BivD %in% c("C0","C90","C180","C270")){


c.copula.be1 <- (p1^(-teta) + p2^(-teta) - 1)^((-1/teta) - 1) * ((-1/teta) * (p1^((-teta) - 1) * (-teta)))

c.copula.be2 <- (p1^(-teta) + p2^(-teta) - 1)^((-1/teta) - 1) * ((-1/teta) * (p2^((-teta) - 1) * (-teta)))
  
      
}


if(BivD %in% c("GAL0","GAL90","GAL180","GAL270")){

c.copula.be1 <- p2*(1-1/((-log(p1))^(1+teta)*(1/(-log(p1))^teta+
1/(-log(p2))^teta)^(1+1/teta)))*exp((1/(-log(p1))^teta+
1/(-log(p2))^teta)^-(1/teta))

c.copula.be2 <- p1*(1-1/((-log(p2))^(1+teta)*(1/(-log(p1))^teta+
1/(-log(p2))^teta)^(1+1/teta)))*exp((1/(-log(p1))^teta+
1/(-log(p2))^teta)^-(1/teta))
  
      
}








if(BivD %in% c("G0","G90","G180","G270")){

  c.copula.be1 <- (exp(-((-log(p1))^teta + (-log(p2))^teta)^((1/teta)))* (-log(p1))^(-1 + 
  teta)* ((-log(p1))^teta + (-log(p2))^teta)^(-1 + 1/teta))/p1


  c.copula.be2 <- (exp(-((-log(p2))^teta + (-log(p1))^teta)^((1/teta)))* (-log(p2))^(-1 + 
  teta)* ((-log(p2))^teta + (-log(p1))^teta)^(-1 + 1/teta))/p2


}






if(BivD %in% c("J0","J90","J180","J270")){

  c.copula.be1 <- ((1 - p1)^teta + (1 - p2)^teta - (1 - p1)^teta * (1 - p2)^teta)^((1/teta) - 
    1) * ((1/teta) * ((1 - p1)^(teta - 1) * teta - (1 - p1)^(teta - 
    1) * teta * (1 - p2)^teta))


  c.copula.be2 <- ((1 - p1)^teta + (1 - p2)^teta - (1 - p1)^teta * (1 - p2)^teta)^((1/teta) - 
    1) * ((1/teta) * ((1 - p2)^(teta - 1) * teta - (1 - p1)^teta * 
    ((1 - p2)^(teta - 1) * teta)))

}








if(BivD == "AMH"){

  c.copula.be1 <- p2 * (1 - p1 * teta * (1 - p2)/(1 - teta * (1 - p1) * (1 - p2)))/(1 - 
                  teta * (1 - p1) * (1 - p2))


  c.copula.be2 <- p1 * (1 - p2 * teta * (1 - p1)/(1 - teta * (1 - p1) * (1 - p2)))/(1 - 
                  teta * (1 - p1) * (1 - p2))

 
}







if(BivD == "FGM"){

  c.copula.be1 <- p2 * (1 + teta * (1 - 2 * p1) * (1 - p2))


  c.copula.be2 <- p1 * (1 + teta * (1 - 2 * p2) * (1 - p1))

}




if(BivD %in% c("C90","J90","G90","GAL90") ) {

c.copula.be2     <- 1 - c.copula.be2

} 



if(BivD %in% c("C180","J180","G180","GAL180") ) {

c.copula.be1     <- 1 - c.copula.be1 
c.copula.be2     <- 1 - c.copula.be2

}  


if(BivD %in% c("C270","J270","G270","GAL270") ) {

c.copula.be1     <- 1 - c.copula.be1

}   


c.copula.be2 <- mm(c.copula.be2, min.pr = min.pr, max.pr = max.pr)
c.copula.be1 <- mm(c.copula.be1, min.pr = min.pr, max.pr = max.pr)

list(c.copula.be1 = ifef(c.copula.be1), c.copula.be2 = ifef(c.copula.be2))

}