PickandsEstimator {RobExtremes} | R Documentation |
Function to compute Pickands estimates for the GPD and GEVD
Description
Function PickandsEstimator
computes Pickands estimator
(for the GPD and GEVD) at real data and returns an object of class Estimate
.
Usage
PickandsEstimator(x, ParamFamily=GParetoFamily(), alpha=2,
name, Infos, nuis.idx = NULL,
trafo = NULL, fixed = NULL, na.rm = TRUE,
...)
.PickandsEstimator(x, alpha=2, GPD.l = TRUE)
Arguments
x |
(empirical) data |
alpha |
numeric |
ParamFamily |
an object of class |
name |
optional name for estimator. |
Infos |
character: optional informations about estimator |
nuis.idx |
optionally the indices of the estimate belonging to nuisance parameter |
fixed |
optionally (numeric) the fixed part of the parameter |
trafo |
an object of class |
na.rm |
logical: if |
... |
not yet used. |
GPD.l |
logical: if |
Details
The actual work is done in .PickandsEstimator
.
The wrapper PickandsEstimator
pre-treats the data,
and constructs a respective Estimate
object.
Value
.PickandsEstimator |
A numeric vector of length |
PickandsEstimator |
An object of S4-class |
Note
The scale estimate we use, i.e., with scale =
and shape =
, we estimate scale by
, differs from
the one given in the original reference, where it was
.
The one chosen here avoids taking differences
hence does not require
; this leads to
(functional) breakdown point (bdp)
which is independent , whereas the original setting leads to
a bdp which is depending on
. As a consequence our setting, the bdp-optimal choice of
for GDP is
leading to bdp
, and
for GEVD leading to bdp
. For comparison, with the
original setting, at
, this gives optimal bdp's
and
for GPD and GEVD, respectively.
The standard choice of
such that
gives the median (
in the GPD and
in the GEVD) in our setting gives
bdp's of
and
for GPD and GEVD, respectively, and
in the original setting, at
, gives bdp's
and
.
Author(s)
Nataliya Horbenko nhorbenko@gmail.com,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
References
Ruckdeschel, P. and Horbenko, N. (2012): Yet another breakdown point notion:
EFSBP –illustrated at scale-shape models. Metrika, 75(8),
1025–1047. doi:10.1007/s00184-011-0366-4.
Pickands, J. (1975): Statistical inference using extreme order statistics.
Ann. Stat. 3(1), 119–131.
See Also
ParamFamily-class
, ParamFamily
,
Estimate-class
Examples
## (empirical) Data
set.seed(123)
x <- rgpd(50, scale = 0.5, shape = 3)
y <- rgev(50, scale = 0.5, shape = 3)
## parametric family of probability measures
P <- GParetoFamily(scale = 1, shape = 2)
G <- GEVFamily(scale = 1, shape = 2)
##
PickandsEstimator(x = x, ParamFamily = P)
PickandsEstimator(x = y, ParamFamily = G)