Generating function for Weibull family

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Description

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

Usage

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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 Matthias.Kohl@stamats.de
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
Nataliya Horbenko nataliya.horbenko@itwm.fraunhofer.de

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. (2011): Optimally-Robust Estimators in Generalized Pareto Models. ArXiv 1005.1476. To appear at Statistics. 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.

See Also

L2ParamFamily-class, Weibull-class

Examples

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

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