Generates an object of class "L2ScaleFamily".
L2ScaleFamily(scale = 1, loc = 0, name, centraldistribution = Norm(),
locscalename = c("loc", "scale"), modParam, LogDeriv,
L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm,
L2derivDistrSymm, trafo, .returnClsName = NULL)Object of class "L2ScaleFamily"
positive number: scale parameter of the model
numeric: location parameter of the model
character: name of the parametric family.
object of class "AbscontDistribution":
central distribution; we assume from the beginning, that centraldistribution
is symmetric about \(0\)
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".
optional function: mapping from the parameter space
(represented by "param") to the distribution space
(represented by "distribution").
function with argument x: the negative logarithmic
derivative of the density of the central distribution; if missing, it is
determined numerically using numeric differentiation.
object of class "UnivariateDistribution":
distribution of the L2derivative at the central distribution
object of class "PosSemDefSymmMatrix":
Fisher information of the model at the "standard" parameter value
object of class "DistributionSymmetry":
symmetry of distribution.
object of class "FunSymmList":
symmetry of the maps contained in L2deriv
object of class "DistrSymmList":
symmetry of the distributions contained in L2derivDistr
matrix or function in param: transformation of the parameter
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.
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
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.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2ScaleFamily-class
F1 <- L2ScaleFamily()
plot(F1)
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