RobExtremes (version 1.3.0)

WeibullFamily: Generating function for Weibull family

Description

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

Usage

WeibullFamily(scale = 1, shape = 0.5, of.interest = c("scale", "shape"),
       p = NULL, N = NULL, trafo = NULL, start0Est = NULL, withPos = TRUE,
       withCentL2 = FALSE, withL2derivDistr  = FALSE, ..ignoreTrafo = FALSE)

Value

Object of class "WeibullFamily"

Arguments

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?

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 speeds up computations).

..ignoreTrafo

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

Author

Matthias Kohl
Peter Ruckdeschel
Nataliya Horbenko

Details

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

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. 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. 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. tools:::Rd_expr_doi("10.1007/s00184-011-0366-4").

See Also

L2ParamFamily-class, Weibull-class

Examples

(G1 <- WeibullFamily())
FisherInfo(G1)
checkL2deriv(G1)