R/dbgpd_ct.R

In mgpd: mgpd: Functions for multivariate generalized Pareto distribution (MGPD of Type II)

dbgpd_ct <-
function(x,y,mar1=c(0,1,0.1),mar2=c(0,1,0.1),a=1/2,b=1/2,...)
{
Be1               = function(x) pbeta(x,a+1,b)
Be2               = function(x) pbeta(x,a,b+1)
d1Be1             = function(x) dbeta(x,a+1,b)
d1Be2             = function(x) dbeta(x,a,b+1)
d2                = function(x,a1,b1) x^(a1-1)*(a1-1)*(1-x)^(b1-1)/(x*beta(a1, b1))-x^(a1-1)*(1-x)^(b1-1)*(b1-1)/((1-x)*beta(a1, b1))
d2Be1             = function(x) d2(x,a+1,b)
d2Be2             = function(x) d2(x,a,b+1)
Qxy               = function(x,y) a*1/y/(a*1/y+b*1/x)
dxQxy             = function(x,y) a*b/(y*(a/y+b/x)^2*x^2)
dyQxy             = function(x,y) -a/(y^2*(a/y+b/x))+a^2/(y^3*(a/y+b/x)^2)
dxdyQxy           = function(x,y) -a*b/(y^2*(a/y+b/x)^2*x^2)+2*a^2*b/(y^3*(a/y+b/x)^3*x^2)
mu                = function(x,y) 1/x*(1-Be1(Qxy(x,y)))+1/y*Be2(Qxy(x,y))
dxdymu            = function(x,y)
1/x^2*d1Be1(Qxy(x,y))*dyQxy(x,y)-
1/x*d2Be1(Qxy(x,y))*dxQxy(x,y)*dyQxy(x,y)-
1/x*d1Be1(Qxy(x,y))*dxdyQxy(x,y)-
1/y^2*d1Be2(Qxy(x,y))*dxQxy(x,y)+
1/y*d2Be2(Qxy(x,y))*dxQxy(x,y)*dyQxy(x,y)+
1/y*d1Be2(Qxy(x,y))*dxdyQxy(x,y)

                  param         = as.numeric(c(mar1,mar2,a,b))
                  mux           = param[1]; muy    = param[4]
                  sigx          = param[2]; sigy   = param[5]
                  gamx          = param[3]; gamy   = param[6]
                  a             = param[7]; b      = param[8]
                  
hxy               = NULL
error             = FALSE 
if(sigx<0 | sigy<0 | a<0 | b<0 ) error = TRUE
if(!error){
                  hxy           = NA
                  tx            = (1+gamx*(x-mux)/sigx)^(1/gamx)
                  ty            = (1+gamy*(y-muy)/sigy)^(1/gamy)
                  tx0           = (1+gamx*(-mux)/sigx)^(1/gamx)
                  ty0           = (1+gamy*(-muy)/sigy)^(1/gamy)
                  dtx           = (1/sigx)*pmax((1+gamx*(x-mux)/sigx),0)^(1/gamx-1)
                  dty           = (1/sigy)*pmax((1+gamy*(y-muy)/sigy),0)^(1/gamy-1)
                  c0            = -mu(tx0,ty0)
                  hxy           = 1/c0*dxdymu(tx,ty)*dtx*dty
                  hxy           = as.numeric(hxy*(1-((x<0)*(y<0))))
}else stop("invalid parameter(s)")
hxy
}