distrMod: L2ScaleUnknownLocationFamily – R documentation

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L2ScaleUnknownLocationFamily

Generating function for L2LocationScaleFamily-class in nuisance situation

Description

Generates an object of class "L2LocationScaleFamily" in the situation where scale is main, location nuisance parameter.

Usage

L2ScaleUnknownLocationFamily(loc = 0, scale = 1, name, centraldistribution = Norm(),
                      locscalename = c("loc", "scale"), modParam, LogDeriv,  
                      L2derivDistr.0, FisherInfo.0, distrSymm, L2derivSymm, 
                      L2derivDistrSymm, trafo, .returnClsName = NULL)

Arguments

`loc`	numeric: location parameter of the model.
`scale`	positive number: scale of the model.
`name`	character: name of the parametric family.
`centraldistribution`	object of class `"AbscontDistribution"`: central distribution; we assume by default, that centraldistribution is symmetric about 0
`modParam`	optional function: mapping from the parameter space (represented by `"param"`) to the distribution space (represented by `"distribution"`).
`locscalename`	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"`
`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`	list of length 2 of objects of class `"UnivariateDistribution"`: (marginal) distributions of the coordinates 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 `L2LocationScaleFamily`; but, internally, this generating function is also used to produce objects of class `NormalLocationScaleFamily`, `CauchyLocationScaleFamily`.

Details

If name is missing, the default “L2 scale family with unknown location (as nuisance)” 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 L2ScaleUnknownLocationFamily. 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.

Value

Object of class "L2LocationScaleFamily"

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

References

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

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

Examples

F1 <- L2ScaleUnknownLocationFamily()
plot(F1)

distrMod

Object Oriented Implementation of Probability Models

v2.8.4

LGPL-3

Authors

Matthias Kohl [aut, cph], Peter Ruckdeschel [cre, cph], R Core Team [ctb, cph] (for source file 'format.perc')

Initial release

2020-03-06