WeibullFamily {RobExtremes}

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)

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.

Details

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

Value

Object of class "WeibullFamily"

Author(s)

Matthias Kohl [e-mail]
Peter Ruckdeschel [e-mail]
Nataliya Horbenko [e-mail]

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. 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. 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. doi:10.1007/s00184-011-0366-4.

See Also

L2ParamFamily-class, Weibull-class

Examples

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