if (!exists("supp")) {supp = new.env()}
with(supp, {
#PDF
pdf.gpd=function(x,k,alpha) {
if (!k==0) {
1/alpha*(1-k*x/alpha)^(1/k-1)
} else {
1/alpha*e^(-x/alpha)
}
}
#CDF
cdf.gpd=function(x,k,alpha) {
if (!k==0) {
1 - (1 - k*x/alpha)^(1/k)
} else {
1 - exp(-x/alpha)
}
}
# hazard
lamda = function(x, k, alpha){
if (k == 0) {
1/alpha
} else{
1/(alpha - k*x)
}
}
#cumulative hazard
Clamda = function(x, k, alpha){
if (k==0){
x/alpha
} else {
1/k*log(alpha/(alpha - k*x))
}
}
# inverse of cumulative hazard
Clamda.inv = function(h, k, alpha){
if (k==0){
alpha*h
} else {
alpha/k*(1 - exp(-k*h))
}
}
})
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