Nothing
dbgpd_negbilog <-
function(x,y,mar1=c(0,1,0.1),mar2=c(0,1,0.1),a=1/2,b=1/2,...){
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)
###################
## spectral density
###################
w = tx/(tx+ty)
l = length(w)
gma1 = rep(NA,l)
for(i in 1:l)
{
eqn =function(z) (1-a)*(1-w[i])*(1-z)^b-(1-b)*w[i]*z^a
if(w[i] == 0) gma1[i] <- 0 else
if(w[i] == 1) gma1[i] <- 1 else
gma1[i] <- uniroot(eqn, lower = 0, upper = 1,tol = .Machine$double.eps^0.5)$root
}
hdens = function(w,gma=gma1) -((1-a)*(1-gma)*gma^(1-a))/((1-w)*w^2*((1-gma)*a+gma*b))
dxdymu = function(x1,y1) -(x1+y1)^(-3)*hdens(x1/(x1+y1))
################
## V(tx0,ty0)
################
c0 = log(pbvevd(c(0,0), model="negbilog", mar1=c(mux,sigx,gamx), mar2=c(muy,sigy,gamy), alpha=(-a), beta=(-b)))
hxy = 1/c0*dxdymu(tx,ty)*dtx*dty
hxy = as.numeric(hxy*(1-((x<0)*(y<0))))
}else stop("invalid parameter(s)")
hxy
}
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