Add Expected Shortfall Estimates to a GPD Plot

Description

Calculates expected shortfall (tail conditional expectation) estimates and confidence intervals for high quantiles above the threshold in a GPD analysis, and adds a graphical representation to an existing plot.

Usage

1
gpd.sfall(x, pp, ci.p = 0.95, like.num = 50)

Arguments

x

a list object returned by plot.gpd or tailplot

pp

the desired probability for expected shortfall estimate (e.g. 0.99 for the 99th percentile)

ci.p

probability for confidence interval (must be less than 0.999)

like.num

number of times to evaluate profile likelihood

Details

Expected shortfall is the expected size of the loss, given that a particular quantile of the loss distribution is exceeded. The GPD approximation in the tail is used to estimate expected shortfall. The likelihood is reparametrised in terms of the unknown expected shortfall and profile likelihood arguments are used to construct a confidence interval.

See Also

gpd, plot.gpd, tailplot, gpd.q

Examples

1
2
3
4
5
6
7
## Not run: data(danish)
## Not run: out <- gpd(danish, 10)
## Not run: tp <- tailplot(out)
## Not run: gpd.q(tp, 0.999) 
# Estimates 99.9th percentile of Danish fire losses 
## Not run: gpd.sfall(tp, 0.999) 
# Estimates associated expected shortfall for Danish fire losses