As I tried to draw random sample from Hüsler-Reiss density with the following
code,
library(evd)
margins <- cbind(0, 1, seq(-0.5,0.5,0.1))
x <- rbvevd(101, dep = 1.7, model = "hr", mar1 = margins)
[,1] [,2]
[1,] -0.56662298 0.8448505
[2,] 0.55824918 1.0217279
[3,] 0.24741124 0.6684668
[4,] -0.31547985 0.1781680
[5,] 0.69466134 0.2299363
[6,] 3.58035098 2.3489841
[7,] -0.07171582 0.6984240
[8,] 0.54275202 0.7706450
[9,] -1.01611325 -0.6598119
[10,] 0.01010218 0.5329360
[11,] 2.13074835 0.4344
These are the set of observation I got.
If we look into the R documentation for the function rbvevd( ), for Hüsler-Reiss
model, it is clear that the marginals are exponential (see below)
The Husler-Reiss distribution function with parameter dep =
r is
G(z1,z2) = exp(-y1 Phi{r^{-1}+r[log(y1/y2)]/2} - y2
Phi{r^{-1}+r[log(y2/y1)]/2}
where Phi() is the standard normal distribution function and r >
0. Independence is obtained in the limit as r approaches zero.
Complete dependence is obtained as r tends to infinity.
But if we look into a sample set it has negative values too but it cannot be.
And more over exponential margins are obtained after take exponential
transformation for Gumbel margins. But for these data set we cannot take
reverse transformation, that is, -log and to get back original model.
Please clarify whether the samples are drawn with Gumbel margins or exponential
margins.
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