distrMod (version 2.5.3)

L2ScaleFamily: Generating function for L2ScaleFamily-class

Description

Generates an object of class "L2ScaleFamily".

Usage

L2ScaleFamily(scale = 1, loc = 0,  name, centraldistribution = Norm(), locscalename = c("loc", "scale"), modParam, LogDeriv,   L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm,  L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

scale

positive number: scale parameter of the model

loc

numeric: location parameter of the model

name

character: name of the parametric family.

centraldistribution

object of class "AbscontDistribution": central distribution; we assume from the beginning, that centraldistribution is symmetric about $0$

locscalename

a character vector of length 1 or 2 containing the names of the scale resp. of location and scale parameter; if length is 2, locscalename is either unnamed, then order must be c(scale,loc), or named, then names must be "loc" and "scale".

modParam

optional function: mapping from the parameter space (represented by "param") to the distribution space (represented by "distribution").

LogDeriv

function with argument x: the negative logarithmic derivative of the density of the central distribution; if missing, it is determined numerically using numeric differentiation.

L2derivDistr.0

object of class "UnivariateDistribution": distribution of the L2derivative at the central distribution

FisherInfo.0

object of class "PosSemDefSymmMatrix": Fisher information of the model at the "standard" parameter value

distrSymm

object of class "DistributionSymmetry": symmetry of distribution.

L2derivSymm

object of class "FunSymmList": symmetry of the maps contained in L2deriv

L2derivDistrSymm

object of class "DistrSymmList": symmetry of the distributions contained in L2derivDistr

trafo

matrix or function in param: transformation of the parameter

.returnClsName

the class name of the return value; by default this argument is NULL whereupon the return class will be L2ScaleFamily; but, internally, this generating function is also used to produce objects of class NormScaleFamily, ExpScaleFamily, and LnormScaleFamily.

Value

"L2ScaleFamily"

Details

If name is missing, the default “L2 scale family” is used. The function modParam is optional. If it is missing, it is constructed from centraldistribution using the scale structure of the model. Slot param is filled accordingly with the argument trafo passed to L2ScaleFamily. In case L2derivDistr.0 is missing, L2derivDistr is computed via imageDistr, else L2derivDistr is assigned L2derivDistr.0, coerced to "UnivariateDistributionList". In case FisherInfo.0 is missing, Fisher information is computed from L2deriv using E. If distrSymm is missing, it is set to symmetry about loc. If L2derivSymm is missing, it is set to no symmetry, and if L2derivDistrSymm is missing, it is set to no symmetry.

References

Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.

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

See Also

L2ScaleFamily-class

Examples

F1 <- L2ScaleFamily()
plot(F1)