GEVFamily

0th

Percentile

Generating function for families of Generalized Extreme Value distributions

Generates an object of class "GEVFamily" which represents a Generalized EV family.

Keywords
models
Usage
GEVFamily(loc = 0, scale = 1, shape = 0.5, of.interest = c("scale", "shape"),
          p = NULL, N = NULL, trafo = NULL, start0Est = NULL, withPos = TRUE,
          secLevel = 0.7, withCentL2 = FALSE, withL2derivDistr  = FALSE,
          withMDE = FALSE, ..ignoreTrafo = FALSE, ..withWarningGEV = TRUE)
Arguments
loc

real: known/fixed threshold/location parameter

scale

positive real: scale parameter

shape

positive real: shape parameter

of.interest

character: which parameters, transformations are of interest. possibilites are: "scale", "shape", "quantile", "expected loss", "expected shortfall"; a maximum number of two of these may be selected

p

real or NULL: probability needed for quantile and expected shortfall

N

real or NULL: expected frequency for expected loss

trafo

matrix or NULL: transformation of the parameter

start0Est

startEstimator --- if NULL PickandsEstimator is used

withPos

logical of length 1: Is shape restricted to positive values?

secLevel

a numeric of length 1: In the ideal GEV model, for each observastion \(X_i\), the expression \(1+\frac{{\rm shape}(X_i-{\rm loc})}{{\rm scale}}\) must be positive, which in principle could be attacked by a single outlier. Hence for sample size \(n\) we allow for \(\varepsilon n\) violations, interpreting the violations as outliers. Here \(\varepsilon = {\tt secLevel}/\sqrt{n}\).

withCentL2

logical: shall L2 derivative be centered by substracting the E()? Defaults to FALSE, but higher accuracy can be achieved when set to TRUE.

withL2derivDistr

logical: shall the distribution of the L2 derivative be computed? Defaults to FALSE (to speed up computations).

withMDE

logical: should Minimum Distance Estimators be used to find a good starting value for the parameter search? Defaults to FALSE (to speed up computations). We have seen cases though, where the use of the then employed PickandsEstimator was drastically misleading and subsequently led to bad estimates where it is used as starting value; so where feasible it is a good idea to also try argument withMDE=TRUE for control purposes.

..ignoreTrafo

logical: only used internally in kStepEstimator; do not change this.

..withWarningGEV

logical: shall warnings be issued if shape is large?

Details

The slots of the corresponding L2 differentiable parameteric family are filled.

Value

Object of class "GEVFamily"

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.

M.~Kohl, P. Ruckdeschel, H.~Rieder (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333--354.

Ruckdeschel, P. and Horbenko, N. (2012): Yet another breakdown point notion: EFSBP --illustrated at scale-shape models. Metrika, 75(8), 1025--1047.

See Also

L2ParamFamily-class, '>GPareto

Aliases
  • GEVFamily
Examples
# NOT RUN {
(G1 <- GEVFamily())
FisherInfo(G1)
checkL2deriv(G1)
# }
Documentation reproduced from package RobExtremes, version 1.2.0, License: LGPL-3

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