This file contains detailed comments on the demo soe9,
which presents examples from Chapter Nine of the text
"Statistics of Extremes: Theory and Applications". The 
R code used in the demo is contained in the file
demo/soe9.R. The demo can be run from R using the code
demo(soe9).

Comments:

1) Differences from the text will inevitably exist due
to the use of different numerical algorithms and random
number generation. In particular, the optimisation 
routines used to derive mles will be different, and
the componentwise maxima will be different since they
are derived using random permutations.

2) The functions use the empirical transform rank/(n+1),
which will differ from the definition in the text when
there are ties in the data, since rank averages over the
ties. Additionally, the R function quantile is used for
the empirical quantile function. This function uses
linear interpolation between data points, so e.g. the
quantile curve plot in Figure 9.6 (using empirical 
margins) will not be a step function.

3) The evd package uses the dependence function A(t), but 
the definition used in the text is B(t) = A(1-t). This
means that the argument rev must be set to TRUE for all
asymmetric models excluding the asymmetric mixed model.
The exclusion occurs because the latter model is 
specified on the dependence function itself, so the
different definitions lead to a reversal of the margins
of its distribution function.

4) Some models are parameterised differently in the text.
For the negative logistic models, they use r = -1/dep.
For the Husler-Reiss (Gaussian) model, they use lambda =
1/dep. The parameterisation of the asymmetric mixed model
is also implicitly different due to the different
dependence function definitions (see 3).

5) The evd package only implements empirical margins for
non-parametric estimators. It does not explicitly implement
empirical margins for parametric models. The text uses only
empirical margins and hence there are some differences, as
follows.

5i) The data is scaled so that it represents $100000 units 
rather than $1 units. This yields numerically stable 
likelihood optimisations. To recover the mles for the 
original data, simply multiply the marginal location and 
scale parameter estimates by 100000.  

5ii) Figure 9.5(b) and the corresponding likelihood ratio
tests use parametric gev margins, unlike the text.

5iii) I have added additional examples showing how to 
calculate the score test for independence with gev margins,
and showing Figure 9.6 with gev margins.

6) Table 9.2 and Figure 9.8 use two undocumented features
of the package. One: the likelihood argument of fbvpot,
which allows implementation of the point process likelihood.
Two: the pot method of abvnonpar, which allows computation
of the peaks-over-threshold non-parametric estimator of
the dependence function in equations (9.72) and (9.58).

7) In Figures 9.9 and 9.10 the demo uses confidence intervals 
based on normal approximations.

8) Figure 9.11 has been excluded: there is no function in evd 
which plots this explicitly, and using basic R code would
be (a) excessively long, because the variance expressions are
very complicated, and (b) confusing, because the expressions
are not given in the text.