[R] Extreme Value Bivariate Point Process Model

[Ron Burns]

Dear All-

I am looking at the bivariate point process model for extreme values as 
described in Section 8.3.2 of Coles book.  I am stuck at a very low 
level in being unable to reproduce the initial step of transforming the 
data to unit Frechet  margins.   In particular, I am unable  to 
reproduce the wave-surge pairs distribution after transformation to 
Frechet scale (Figure 8.6 of Coles book).  Here is what I am doing:

library(ismev)
data(wavesurge)
wave <- wavesurge[,1]
surge <- wavesurge[,2]
plot(wave,surge, pch=20)  ## reproduces Coles fig 1.11
## do the GEV fit
w <- gev.fit(wave)
s <- gev.fit(surge)
### Transform to frechet variable using
GEV2frechet <- function (x, loc, scale, shape)
  pmax(1 + shape * (x - loc)/scale, 0)^(1/shape)
Zw <- GEV2frechet(wave,w$mle[1],w$mle[2],w$mle[3])
Zs <- GEV2frechet(surge,s$mle[1],s$mle[2],s$mle[3])
## Check point distribution with Figure 8.6
plot(log(Zw),log(Zs),pch=20)
### Very different

The above seems to be quite straightforward and I am at a loss for what 
is going wrong.  Perhaps someone can get me pointed in the right 
direction.  Thanks in advance for your consideration and help.

Regards
    Ron Burns

-- 
R. R. Burns
Physicist (Retired)
Oceanside, CA