gentruk {vfcp}

Creating an object for CDF and copula survival

Description

For given inputs, the coordinates of the object defined by the CDF and the survival function for the copula object are created.

Usage

gentruk(tht, fm, C, pro)

Arguments

tht

Copula parameter. If fam = "fgm", it must be a vector of size dm*(dm-1)/2 + 1.

fm

Family name copula. These can be: "clayton", "gumbel", "frank", "joe", "amh", "fgm".

C

Probability value of the copula. Single value.

pro

Numeric vector. Its pro[1:k] are upper values of the u. Next pro[-c(1:k)] are then all greater than or equal to 1.

Value

A list with components as trimeze value.

Author(s)

Josef Brejcha

Examples

tht = 0.6
cx = c(0.025, 0.05, 0.1, 0.15, 0.25)
pro = c(0.99999, 0.9999, 0.999, 0.99, 24, 16, 8, 4)
dm = 2
fam = "fgm"
marg = c("weibull", "betapr")
xo = c(200, 2.75, 16.5, 6.60)
e12 = vfenuo(marg, xo)
p = numeric(length(cx))
x12 = qweibull(0.975, scale = xo[1], shape = xo[2])
y12 = qbetapr(0.975, shape1 = xo[3], shape2 = xo[4])
mtit = paste(fam, " ... ", marg[1], "(", xo[1], ", ", xo[2], ")",
						 " ", marg[2], "(", xo[3], ", ", xo[4], ")",
						 sep = "")
plot(NULL, NULL, xlim = c(0, x12), ylim = c(0, y12),
     xlab = paste("x, E[x] = ", round(e12[1], 2)),
		 ylab = paste("y, E[y] = ", round(e12[2], 2)),
		 main = mtit)
points(e12[1], e12[2], pch = 20)
abline(h = e12[2], v = e12[1])
grid(col = "grey50")
#===========================
kop2 = kopula(fam, tht, dm)
fmc = c("", "", "clayton", "gumbel", "frank", "joe")
pro = c(0.999999, 0.99999, 0.9999, 16, 8, 4, 2)
tm3 = list()
tmk = list()
for (k in 1:length(cx)){
  tm3 = gentruk(tht, fm=fam, C=cx[k], pro)
  tmk[[k]] = tm3
}
p = prosim(C = cx, fam, tht, dm, no = 100000)
# =============
xa = c("u")
ya = c("v")
for (k in 1:length(cx)){
  mspx = vfmrg(rdj=marg, i=1, cosi=tmk[[k]]$sp$s1, yo=xo, cdf=TRUE)
  mspy = vfmrg(rdj=marg, i=2, cosi=tmk[[k]]$sp$s2, yo=xo, cdf=TRUE)
  mcpx = vfmrg(rdj=marg, i=1, cosi=tmk[[k]]$cp$c1, yo=xo, cdf=TRUE)
  mcpy = vfmrg(rdj=marg, i=2, cosi=tmk[[k]]$cp$c2, yo=xo, cdf=TRUE)
  lines(mspx,mspy, col=k)
  lines(mcpx, mcpy, col = k)
}
  legend("topleft", legend = c("C", cx), text.col = c(1, 1:length(cx)),
         bty = "n")
  legend("topright", legend = c("p", round(p, 4)),
         text.col = c(1, 1:length(cx)), bty = "n")