Generates an object of class "L2LocationScaleFamily"
.
L2LocationScaleFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
locscalename = c("loc", "scale"), modParam, LogDeriv,
L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm,
L2derivDistrSymm, trafo, .returnClsName = NULL)
Object of class "L2LocationScaleFamily"
numeric: location parameter of the model.
positive number: scale of the model.
character: name of the parametric family.
object of class "AbscontDistribution"
:
central distribution; we assume by default, that centraldistribution
is symmetric about \(0\)
optional function: mapping from the parameter space
(represented by "param"
) to the distribution space
(represented by "distribution"
).
a character vector of length 2 containing the names
of the location and scale parameter; either unnamed, then order must
be c(loc,scale)
, or named, then names must be "loc"
and
"scale"
function with argument x
: the negative logarithmic
derivative of the density of the central distribution; if missing, it is
determined numerically using numeric differentiation.
list of length 2 of objects of class "UnivariateDistribution"
:
(marginal) distributions of the coordinates 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
L2LocationScaleFamily
; but, internally, this generating function is also
used to produce objects of class NormalLocationScaleFamily
,
CauchyLocationScaleFamily
.
Matthias Kohl Matthias.Kohl@stamats.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
If name
is missing, the default
“L2 location and scale family” is used.
The function modParam
is optional. If it is missing, it is
constructed from centraldistribution
using the location and
scale structure of the model.
Slot param
is filled accordingly with the argument
trafo
passed to L2LocationScaleFamily
.
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, its location and scale components are set
to no symmetry , respectively.
if L2derivDistrSymm
is missing, its location and scale components are set
to no symmetry, respectively.
Rieder, H. (1994) Robust Asymptotic Statistics. New York: Springer.
Kohl, M. (2005) Numerical Contributions to the Asymptotic Theory of Robustness. Bayreuth: Dissertation.
L2LocationScaleFamily-class
F1 <- L2LocationScaleFamily()
plot(F1)
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