internals_for_distrMod: Internal functions of package distrMod

Description

These functions are used internally by package ``distrMod''.

Usage

.inArgs(arg, fct)
.isUnitMatrix(m)
.csimpsum(fx)
.validTrafo(trafo, dimension, dimensionwithN)
.CvMMDCovariance(L2Fam, param, mu = distribution(L2Fam),
                 withplot = FALSE, withpreIC = FALSE,
                 N = 1021, rel.tol=.Machine$double.eps^0.3,
                 TruncQuantile = getdistrOption("TruncQuantile"), 
                 IQR.fac = 15, ..., diagnostic = FALSE)
.oldCvMMDCovariance(L2Fam, param, mu = distribution(L2Fam),
                 withplot = FALSE, withpreIC = FALSE,
                 N = getdistrOption("DefaultNrGridPoints")+1,
                 rel.tol=.Machine$double.eps^0.3,
                 TruncQuantile = getdistrOption("TruncQuantile"),
                 IQR.fac = 15, ...)
.CvMMDCovarianceWithMux(L2Fam, param, withplot = FALSE, withpreIC = FALSE,
                        N = 1021, rel.tol=.Machine$double.eps^0.3,
                        TruncQuantile = getdistrOption("TruncQuantile"),
                        IQR.fac = 15, ..., x=NULL)
.show.with.sd(est, s)
.getLogDeriv(distr, 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
                         IQR.fac = getdistrExOption("IQR.fac"))
.deleteDim(x)

Value

.getLogderiv: a function in one argument x --- the negative logarithmic derivative of the density
.inArgs: logical (length 1)
.csimpsum: numeric (of length half the input length)
.isUnitMatrix: logical (length 1)
.validTrafo: logical (length 1)
.CvMMDCovariance: corresponding as. [co]variance of the corresponding Minimum CvM estimator or list withcomponents preIC and var ---see above
.show.with.sd: invisible()
.deleteDim: vector x without dim attribute

Arguments

arg: a formal argument as character
fct: a function
m: a matrix
est: an estimator; usually a vector
s: a standard deviation
trafo: an object of class MatrixorFunction
dimension: a numeric --- length of main part of the parameter
dimensionwithN: a numeric --- length of main and nuisance part of the parameter
L2Fam: an object of class L2ParamFamily --- for which we want to determine the IC resp. the as. [co]variance of the corresponding Minimum CvM estimator
param: an object of class ParamFamParameter, the parameter value at which we want to determine the IC resp. the as. [co]variance of the corresponding Minimum CvM estimator
mu: an object of class UnivariateDistribution: integration measure (resp. distribution) for CvM distance
rel.tol: relative tolerance for distrExIntegrate.
TruncQuantile: quantile for quantile based integration range.
lowerTruncQuantile: lower quantile for quantile based integration range.
upperTruncQuantile: upper quantile for quantile based integration range.
IQR.fac: factor for scale based integration range (i.e.; median of the distribution \(\pm\)IQR.fac\(\times\)IQR).
withplot: logical: shall we plot corresponding ICs?
withpreIC: logical: shall we return a list with components preIC and var or just var; here var is the corresponding asymptotic variance and preIC the corresponding EuclRandVarList featuring as argument Curve in ICs of package RobAStBase
N: a numeric: the number of gridpoints for constructing the \(\mu\)- resp. \(P_\theta\)-``primitive'' function
fx: a vector of function evaluations multiplied by the gridwidth
distr: an object of class AbscontDistribution
...: further argument to be passed through --- so .CvMMDCovariance can digest more arguments.
x: in deleteDim: a possibly named vector, which may have a dim attribute; in .CvMMDCovarianceWithMux: NULL (default) or the vector with observations to build integration measure \(mu\) as the empirical cdf.
diagnostic: logical; if TRUE, the return value of .CvMMDCovariance obtains an attribute "diagnostic" (usually a lengthy list) with diagnostic information on the call and on the integration, the latter inherited from the calls to distrExIntegrate and E in this function. Depending on the actually used E method, this comprises entries method ("integrate" or "GLIntegrate"), result (the complete return value of the integration method), args (the args with which the integration method was called), and time (the time to compute the integral).

Author

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de Matthias Kohl Matthias.Kohl@stamats.de

Details

.inArgs (borrowed from package distr) checks whether an argument arg is a formal argument of fct --- not vectorized.

.csimpsum (borrowed from package distr) produces a primitimive function out of function evaluations by means of vectorized Simpson quadrature method, returning already the function values of the prime function on a grid; it is to mimick the behaviour of cumsum.

.isUnitMatrix checks whether the argument is a unit matrix.

.validTrafo checks whether the argument is a valid transformation.

.CvMMDCovariance determines the IC resp. the as. [co]variance of the corresponding Minimum CvM estimator (numerical integration is done on quantile scale).

.oldCvMMDCovariance determines the IC resp. the as. [co]variance of the corresponding Minimum CvM estimator (numerical integration is done on the original scale). .CvMMDCovariance is a wrapper to .CvMMDCovariance which uses emp. cdf as mu.

.show.with.sd is code borrowed from print.fitdistr in package MASS by B.D. Ripley. It pretty-prints estimates with corresponding sd's below.

.getLogDeriv determines numerically the negative logarithmic derivative of the density of distribution distr; to this end uses D1ss, D2ss from Martin Maechler's package sfsmisc.