mdaPlots {fExtremes} | R Documentation |
This is a collection of functions for the estimation of the tail
index of extreme data using the maximum domain of attraction, MDA,
method. Included are the Pickands, Einmal-Decker-deHaan, and Hill
estimators together with several plot variants.
The functions are:
1 | hillPlot | shape parameter and Hill estimate of the tail index, |
2 | shaparmPlot | variation of shape parameter with tail depth. |
hillPlot(x, option = c("alpha", "xi", "quantile"), start = 15, end = NA, reverse = FALSE, p = NA, ci = 0.95, autoscale = TRUE, labels = TRUE, ...) shaparmPlot(x, revert = FALSE, standardize = FALSE, tails = 0.01*(1:10), doplot = <<see below>>, which = <<see below>>, doprint = TRUE, both.tails = TRUE, xi.range = c(0, 10), alpha.range = c(-0.5, 1.5))
x |
[hillPlot][shaparmPlot] - the data from which to calculate the shape parameter, a numeric vector. |
autoscale |
[hillPlot] -
whether or not plot should be automatically
scaled; if not, xlim and ylim graphical
parameters may be entered.
|
ci |
[hillPlot] -
probability for asymptotic confidence band; for no
confidence band set ci to zero.
|
labels |
[hillPlot] - whether or not axes should be labelled. |
option |
[hillPlot] -
whether alpha , xi (1/alpha) or
quantile (a quantile estimate) should be plotted.
|
p |
[hillPlot] -
probability required when option quantile is
chosen.
|
reverse |
[hillPlot] -
whether plot is to be by increasing threshold, TRUE , or
increasing number of order statistics FALSE .
|
start, end |
[hillPlot] - lowest and highest number of order statistics at which to plot a point. |
... |
[hillPlot] - other graphics parameters. |
alpha.range, xi.range |
[saparmPlot] - plotting ranges. |
both.tails |
[saparmPlot] - a logical, decides whether or not both tails should be investigated. By default TRUE. If FALSE only the lower tail will be investigated. |
doplot |
[saparmPlot] -
a vector of logicals of the same lengths as tails
defining for wich tail depths plots should be created,
by default plots will be generated for a tail depth of 5
percent. By default c(FALSE, FALSE, FALSE, FALSE,
TRUE, FALSE, FALSE, FALSE, FALSE, FALSE) .
|
doprint |
[saparmPlot] -
a logical, decides whether or not for all tail depths the
result for the shape parameter 1/alpha should be
printed.
|
revert |
[saparmPlot] -
a logical value, by default FALSE, if set to TRUE the
sign of the vector will be reverted: x = -x .
|
standardize |
[saparmPlot] -
a logical value, by default FALSE, if set to
TRUE the vector x will be standardized:
x = (x-mean(x))/sqrt(var(x)) .
|
tails |
[saparmPlot] - a numeric vector of tail depths to be considered; by default ten values ranging from 0.1 to 1.0 in steps of 0.1 corresponding to values ranging from 1 to 10 percent. |
which |
[saparmPlot] -
a vector of 3 logicals indicating which plots from the
three methods will be created. The first entry decides
for the Pickands estimator, the second for the Hill
estimator, and the last for the Deckers-Einmahl-deHaan
estimator. By default all three will be created.
By default c(TRUE, TRUE, TRUE) .
|
Hill Plot:
The function hillPlot
investigates the shape parameter and
plots the Hill estimate of the tail index of heavy-tailed data, or
of an associated quantile estimate. This plot is usually calculated
from the alpha perspective. For a generalized Pareto analysis of
heavy-tailed data using the gpdFit
function, it helps to
plot the Hill estimates for xi
.
Shape Parameter Plot:
The function shaparmPlot
investigates the shape parameter and
plots for the upper and lower tails the shape parameter as a function
of the taildepth. Three approaches are considered, the Pickands
estimator, the Hill estimator, and the
Decker-Einmal-deHaan estimator.
hillPlot
displays a plot.
shaparmPlot
returns a list with one or two entries, depending on the
selection of the input variable both.tails
. The two
entries upper
and lower
determine the position of
the tail. Each of the two variables is again a list with entries
pickands
, hill
, and dehaan
. If one of the
three methods will be discarded the printout will display zeroes.
Alec Stephenson for R's evir package,
Alexander Mcneil for the original EVIS code,
Diethelm Wuertz for this R-port.
Coles S. (2001); Introduction to Statistical Modelling of Extreme Values, Springer.
Embrechts, P., Klueppelberg, C., Mikosch, T. (1997); Modelling Extremal Events, Springer.
## hillPlot - xmpExtremes("\nStart: Hill Estimator >") # Hill plot of heavy-tailed Danish fire insurance data # and BMW stock data for estimated 0.999 quantile par(mfrow = c(2, 2)) data(bmw) hillPlot(bmw) hillPlot(bmw, option = "quantile", end = 500, p = 0.999) data(danish) hillPlot(danish) hillPlot(danish, option = "quantile", end = 500, p = 0.999) ## shaparmPlot - xmpExtremes("\nNext: Shape Parameter Plots >") par(mfcol = c(3, 2), cex = 0.6) data(bmw) shaparmPlot(bmw) ## shaparmPlot - xmpExtremes("\nNext: Simulated Frechet Data >") par(mfcol = c(3, 2), cex = 0.6) set.seed(4711) x = rgev(10000, xi = 1/4) shaparmPlot(x, revert = TRUE, both.tails = FALSE) lines(c(0.01, 0.1), c(4, 4), col = "steelblue3") # True Value