GParetoFamily: Generating function for Generalized Pareto families

View source: R/GParetoFamily.R

GParetoFamilyR Documentation

Generating function for Generalized Pareto families

Description

Generates an object of class "GParetoFamily" which represents a Generalized Pareto family.

Usage

GParetoFamily(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)

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 medkMADhybr 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).

..ignoreTrafo

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

Details

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

Value

Object of class "GParetoFamily"

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
Nataliya Horbenko nhorbenko@gmail.com

References

Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation. https://epub.uni-bayreuth.de/id/eprint/839/2/DissMKohl.pdf.

Kohl, M., Ruckdeschel, P., and Rieder, H. (2010): Infinitesimally Robust Estimation in General Smoothly Parametrized Models. Stat. Methods Appl., 19, 333-354. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10260-010-0133-0")}.

Ruckdeschel, P. and Horbenko, N. (2013): Optimally-Robust Estimators in Generalized Pareto Models. Statistics. 47(4), 762-791. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/02331888.2011.628022")}.

Ruckdeschel, P. and Horbenko, N. (2012): Yet another breakdown point notion: EFSBP –illustrated at scale-shape models. Metrika, 75(8), 1025–1047. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00184-011-0366-4")}.

See Also

L2ParamFamily-class, GPareto

Examples

(G1 <- GParetoFamily())
FisherInfo(G1)
checkL2deriv(G1)

RobExtremes documentation built on Feb. 12, 2024, 3:01 a.m.