Optimally Robust Estimation

Optimally robust estimation in general smoothly parameterized models using S4 classes and methods.


News

###############################################################################

News: to package ROptEst

###############################################################################

(first two numbers of package versions do not necessarily reflect package-individual development, but rather are chosen for the RobAStXXX family as a whole in order to ease updating "depends" information)

####################################### version 1.2 #######################################

user-visible CHANGES:

  • slot function modifyIC of the different IC classes gains an argument withMakeIC to be able to adjust this to a higher granularity
  • require more recent versions in DESCRIPTION
  • getBiasIC for signature {HampIC,UncondNeighborhood} no longer has argument withCheck
  • getRiskIC gains argument "..." to pass on arguments to E()
  • the help to robest is more explicit about the usage of argument E.argList at various places in the generator
  • the help to roptest has an extra paragraph explicating the usage of initial.est and start.Par and the different steps done in roptest
  • the input generators genkStepCtrl, genstartCtrl, genstartICCtrl gain argument E.argList to pass on arguments to E()
  • roptest and the wrappers RMX|OBR|MBR|OMSEstimator gain an argument E.argList for arguments to be passed to E() from (a) \code{MDEstimator} (here this additional argument is only used if \code{initial.est} is missing), (b) \code{getStartIC}, and (c) \code{kStepEstimator}. Potential clashes with arguments of the same name in \code{\dots} are resolved by inserting the items of argument list \code{E.argList} as named items, so in case of collisions the item of \code{E.argList} overwrites the existing one from \code{\dots}.
  • roptest and its wrappers RMX|OBR|MBR|OMSEstimator can now also digest robest-arguments arguments \code{startCtrl}, \code{startICCtrl}, and \code{kStepCtrl}, in which case information in these arguments in case of collision overrides information given through the "usual" arguments; this allows for individual settings of \code{E.argList}, \code{withEvalAsVar}, and \code{withMakeIC} for the different steps.
  • roptest and its wrappers RMX|OBR|MBR|OMSEstimator, getStartIC for asGRisk, asBias, RMX, and asAnscombe, as well as the particular checkIC/makeIC methods for ContIC gain argument diagnostic to be able to show diagnostic information on integrations; this information (if argument "diagnostic" is TRUE) is stored in attribute "diagnostic" of the return value
  • accessors "timings" and "kStepTimings" to attributes "timings" and and "kStepTimings" of an object of class "ORobEstimate"

bug fixes

  • an embarrassing error when computing E(X t(X)) (saving the lower half by symmetry) in getInfStand: a[row(a)>col(a)] <- a[row(a)<col(a)] in general is not symmetric... did not bite us so far as the highest dim we considered so far was 3, and the recipe is exact exactly up to dim 3... the exact formula would have been (and is now in the code) a[row(a)>col(a)] <- t(a)[row(a)>col(a)]
  • fix an argument collision in MBRE-method / in call to getInfRobIC_asGRisk, when called from OptIC through getInfRobIC_asBias ("upper" got into ...)

under the hood

  • L2LocationFamily, L2LocationScaleFamily, and L2LocationScaleFamily gain methods for interpolRisk ~> speed up is prepared (only need to store the reference LMs in sysdata.rda) => due to affine equivariance, we only have to store one set of LM's
  • comparePlot has a try catch now for MBRE
  • some buglets in getStartIC
  • some tedious debugging in getStartIClcsc.R
  • clarified if clauses in roptest.new (and removed .with.checkEstClassForParamFamily from dots to be sure)
  • inserted code for time checking (which is inactive usually; only if in kStepEstimator.R in RobAStBase, the respective ##-t-## lines are de-commented the timings are visible as attribute "kStepTimings" in the result of roptest ...) changed now: is always active....
  • now specified that we want to use distr::solve
  • internal function .getComp, determining by symmetry slots which entries in LMs a and A have to be computed, now fills the lower triangle of A with FALSE (was not used so far, but can be used in a faster computation method for checkIC makeIC to determine whether it is cleverer to integrate in k or in p space)
  • several methods (getRiskIC, getBiasIC, getBoundedIC, makeIC, checkIC, modifyIC) gain argument "..." to pass on arguments to E(). This holds in particular for the functions used to compute the optimally-robust ICs, i.e. getInfRob_asBias, getInfRob_asHampel, getInfRob_asGRisk, getInfRob_asAnscombe, leastFavorableRadius, radiusMinimaxIC, and geInfGamma, getInfRad, getInfClip, getInfCent, getInfStand, getInfV, getAsRisk, getReq, (at least as far as multivariate ICs are concerned), .LowerCaseMultivariate, getMaxIneff, getInfRad, getLagrangeMultByIter and getLagrangeMultByOptim
  • new internal helper function .filterEargWEargList is used to filter out arguments from dots which are meant for E()
  • the local .modifyIC0 functions only used to produce the new IC but not for filling slot modifyIC loose argument withMakeIC (and dots) -- this is now done in the outer modifyIC function
  • particular checkIC, makeIC methods for ContICs: They compute the integrals E w, E L w, E LL w using symmetry information through .getComp, and based on these numbers computes does checking / the affine transformation to give the proper pIC. These methods by default are only used if it pays off, i.e., if the number of computed integrals is smaller than in the default method. This can be overriden by argument forceContICMethod.
  • the particular checkIC and makeIC methods gain argument diagnostic to be able to show diagnostic information on integrations
  • roptest, robest, and particular checkIC/makeIC methods for ContIC now if (diagnostic==TRUE) return diagnostic attributes of S3 class "DiagnosticClass"

####################################### version 1.1 #######################################

user-visible CHANGES:

  • new wrapper functions RMXEstimator, OBREstimator, MBREstimator, OMSEstimator
  • plot-methods now have arguments .nonlb to only plot (but not label) some points
  • plot-methods are vectorized to a higher extent in all arguments
  • plot methods now return an S3 object of class \code{c("plotInfo","DiagnInfo")}, i.e., a list containing the information needed to produce the respective plot, which at a later stage could be used by different graphic engines (like, e.g. \code{ggplot}) to produce the plot in a different framework. A more detailed description will follow in a subsequent version.
  • optIC gains argument withMakeIC
  • roptest gains argument withMakeIC
  • getStartIC-methods gain argument withMakeIC
  • cniperPointPlot gains argument withMakeIC
  • genkStepCtrl gains argument withMakeIC
  • DESCRIPTION tag SVNRevision changed to VCS/SVNRevision
  • getRiskIC and getBiasIC gain argument withCheck to speed up things if one does not want to call checkIC

Return value of "roptest"

  • the return value of "roptest", an object of class "kStepEstimate" has a slot "estimate.call" which contains the (matched) call to "roptest"; internally "roptest" calls "robest"; the call to "robest" may be of interest, too, so we have a new slot "robestCall" of class "OptionalCall", ie a call
    or NULL (default); it can be accessed via function robestCall()

Bugfix:

  • argument withMakeIC was not correctly used in roptest.new

under the hood:

  • try to minimize interim output while using roptest- and friends
  • new return class ORobEstimate for optimally robust estimators
  • wherever possible also use q.l internally instead of q to provide functionality in IRKernel
  • fixed all scripts
  • by means of argument modifyICwarn the filling of info slots with warnings is controlled; over all at most one warning is written into the info string

####################################### version 1.0.1 ####################################### user-visible CHANGES:

  • moved getFiRisk from ROptEst to RobAstBase

####################################### version 1.0 #######################################

user-visible CHANGES:

  • title changed to title style / capitalization
  • cniperPointPlot gains capacity to deal with "interpolRisk" - risks
  • cniperPointPlot gains optional pattern substitution (like plot) which can be switched off by argument withSubst

GENERAL ENHANCEMENTS:

under the hood:

  • preparations for evalation of LMs on xi grid for GEVFamilyMuUnknown.
  • new methods for normtype and biastype for interpolRisk, as well as getRiskFctBV => now cniperPointPlot should work for GPD-type data
  • removed ::: internal dependencies (within distr&robast-Fam's of pkgs) by copying respective routines
  • adjusted plot-Method for ICs to include the new argument x.vec
  • enhanced imports in DESCRIPTION by explicating second order imports

BUGFIXES:

  • two bugs in plotWrapper.R in pkgs RobAStBase and ROptEst detected by Misha
  • needed version of RandVar was wrongly specified in ROptEst in the branch 1.0
  • fixed errors detected by Matthias / Misha in AllPlot.R, comparePlot.R, getReq.R
  • fixed issue with updateStep in kStepEstimator when using interpol risks (somehow modifyIC had not been attached in prior steps...)
  • labels did not work correctly, warnings due to calling plot with "withMaxRisk"
  • fixed issue with points plotting in Cniperpoint-plots
  • in wrapper function CniperPointPlot, arguments 'data' and 'alpha.trsp' had not been passed on correctly
  • some changes in wrapper to cniperpointplot
  • fixed an error in cniperPointPlot() -- default for argument risk had not been passed on correctly to cniperCont() ####################################### version 0.9 #######################################

user-visible CHANGES:

  • new wrapper function CniperPointPlot

  • new more modularized user-interface robest

  • roptest (the new one) gains argument withMDE to skip call to MDE when starting estimator is robust anyway;

  • roptest gains argument withEvalAsVar

  • roptest may force logscale when calling kStepEstimator

  • removed argument scalename from arglist of roptest -- it is computed automatically now.

  • added new function 'showdown' to compare some estimator with our rmx estimator by some Monte-Carlo study.

  • assigned result of qqplot to some variable to reduce output

  • generating function genkStepCtrl for control arguments for kStepEstimator gains argument withEvalAsVar

  • similarly genstartCtrl() gains optional argument withMDE

  • optIC gains argument .withEvalAsVar

  • new functionality to determine "optimal" radius (getRadius, getInfRad (the latter an S4method));

GENERAL ENHANCEMENTS:

  • RobASt-Pkgs: DESCRIPTION depends become stricter (requiring distrMod, distrEx, distr >=2.4 to be on the safe side)

  • cleaned DESCRIPTION and NAMESPACE file as to Imports/Depends

  • deleted chm folders --- they are no longer needed

  • delayed evaluation is done to speed up things

  • added argument no.readonly = TRUE in all assignments of type opar <- par();

  • commented out all assignments of type omar$cin <- NULL

  • removed calls to require from R sources and replaced it by directives in the NAMESPACE file

  • all packages get a DESCRIPTION tag "ByteCompile"

  • Suggests field with RobLox and MASS due to a warning by R CMD check

under the hood:

  • added .Rbuildignore

  • Had to add 'importFrom(distr, q)' to NAMESPACE to avoid error with function 'q' inside of 'showdown' - why?!

  • replaced former interface roptest by a new, more modularized one

  • timings in roptest, robest are now optional; at any rate are attached as attribute

  • moved asL1, asL4 risk methods from RobAStBase to ROptEst

  • getStartIC.R

    • cleaned up (deleted unnecessary diagnostic prints) skipped unnecessary steps when dealing with MBRE
    • getStartIC for signature L2ParamFamily,asGRisk gains argument withEvalAsVar
  • getStartIC - method for interpolRisks (and hence internal-getpsi, too) moved from ROptEst to RobExtremes

  • getStartIC now also dispatches on asCov, trASCov, and asBias risk

  • getRiskIC gains example and for signature(IC = "HampIC", risk = "asCov",
    neighbor = "missing", L2Fam = "L2ParamFamily") in 1dim case now uses getInfV() .

  • getRiskIC is careful and first evaluates covariance objects

+++ optIC already contains stubs to use moveL2Fam2RefParam, moveICBackFromRefParam (still some checking necessary before using this really...)

  • modified interval search in leastFavorableRadius and radiusMinimaxIC in case uniroot fails to find zeroes

  • some more try-catches for radiusMinimaxIC (to keep this clean rewritten, with call manipulations) and leastFavorableRadius (only minimal call manipulations -> got longer)

  • getIneffDiff now returns a vector (if called as from radiusMinimaxIC, leastFavorableRadius) with lower and upper inefficiency; difference is computed in local functions now

  • getInfRobIC_asGRisk getInfRobIC_asHampel now get argument .withEvalAsVar and, accordingly only produce calls to generate asyVariances or evaluate them as well

  • getInfClip, signature(clip = "numeric", L2deriv = "UnivariateDistribution", risk = "asSemivar", neighbor = "ContNeighborhood") regains argument biastype as it is called this way in getInfRobIC_asGRisk.R

  • getInfV now always returns a matrix

  • interpolation infrastructure:

    • .mergeF
    • .copyGrid
    • .renameGridName
    • .MakeGridList
    • .saveInterpGrid (with new argument structure / new defaults)
    • .recomputeInterpolators
    • .getLMGrid
    • .RMXE.th
    • .MBRE.th
    • .OMSE.th
  • .recomputeInterpolators, .saveInterpGrid gain argument sysdataWriteFile to be able to write to other files (other than sysdata.rda) => no need anymore to write in separate folders when creating new grids in parallel

  • use of unit tests

BUGFIXES:

  • a minimal correction in getInfRobIC_asGRisk.R
  • in roptest forgot to treat the case when additional arguments are passed to the initial estimator
  • two silly errors in roptest.new.R -> threw error when passed on S4-estimators as starting estimators
  • fixed a bug in in leastFavorableRadius and radiusMinimaxIC
  • .evalListRec was not prepared for length 0
  • some substitute functions have not been passed as arguments...
  • functions where identical in grid..!)
  • a minor error in helper function .check.eps
  • fixed two bugs (for radius 0) in "getInfRobIC", signature(L2deriv = "RealRandVariable", risk = "asGRisk",neighbor = "UncondNeighborhood")
  • cleared bug from ticket #131

####################################### version 0.8 #######################################

USER-VISIBLE CHANGES:

functions/classes:

  • added new Risk class asAnscombe for determining OBRE to given ARE in the ideal model

  • now Anscombe-Risk also works with information standardization ( but is not suited for self-standardization!)

  • new risk asL1 asL4 (for asy. mean absolute error and asy mean power 4 error) with generators etc

  • new method get.asGRisk.fct to obtain a function in r,s,b (s=var^.5) to compute respective as. G-Risk

  • getAsRisk now has (almost) the same signature for different methods (so that in can easily be called when the actual risk is not clear)

  • new helper methods makeIC to apply to functions or list of functions for easily producing (suboptimal) ICs

  • new function getReq for two ICs IC1 and IC2 to compute a radius interval where IC1 is better than IC2 acc. to G-Risk

  • new function getMaxIneff() to compute for any IC of class 'IC' the maximal inefficiency on r in [0,Inf)

scripts/examples:

  • uploaded Script for NbinomFamily

  • added demo script for Normal Location case

  • added calls to getMaxIneff() and getReq() in script to Normal Location

  • examples for asAnscombe (see examples in inst folder (Binomial, Gamma, Nbinom, NormalLocationScale, NormalScale, Poisson);

  • Integrated new example to getReq.Rd and new script AnscombeOrNot.R

  • some modifications/additions needed for the revised version of the corresponding manuscript. names of added scripts were wrong ...

documentation:

  • new references included in help files
  • DESCRIPTION files and package-help files gain a tag SVNRevision to be filled by get[All]RevNr.R from utils in distr

enhancements:

  • filled Feature Request #919 / cniperPointPlot now digests arbitrary plot arguments.

BUG FIXES

  • fixed an issue with lower case solution in information/self-standardization;

  • committed some missing Rd files for Anscombe class

  • fixed some bug in Anscombe-risk for univariate L2deriv

  • fixed a bug in multivariate version of getMaxIneff() included respective examples to Rd file (with sin,cos-IC)

  • a buglet in getInfClip.R

  • fixed the asL1, asL4 issue --- getInfGamma beforehand was defined for asMSE not for asGRisk

  • fixed two bugs in calculation of risks: trAsCov and asCov (for total variation)

  • fixed a little bug in comparePlot if we want to plot pIC's

  • fixed a buglet in asL1 asL4 risks

  • fixed yet another buglet in asL1 risks

  • fixed a little bug in getMaxIneff.R

  • lower and upper interval bounds for search in clipping height in getInfRobIC_asGRisk.R are now selected differently for univariate L2-deriv according to whether risk is asMSE() or not

  • for restoring old par() values, not all attributes may be set; hence deleted them from stored value in plot functions by something like opar$cin <- opar$cra <- opar$csi <- opar$cxy <- opar$din <- NULL

####################################### version 0.7 #######################################

USER-VISIBLE CHANGES:

*** DUALITY BASED optIC-ALGORITHM

-> optional use of alternative algorithm to obtain Lagrange multipliers using duality based optimization -> rewritten algorithm:

  • getInfRob_asGRisk.R now have both an iterative and an optimization
  • getInfRob_asHampel.R algorithm to obtain Lagrange Multipliers; --- i.e. depending on argument OptOrIter (default: iteration as before...) they call getLagrangeMultByOptim resp. getLagrangeMultByIter (unfortunately: optimization is slow; only L-BFGS-B works satisfactory)
  • getInfLM now gains (unfortunately not a good idea as to speed!) the new MSE - optimization routines for obtaining LagrangeMultipliers

*** optIC Solution for general trafo / with nuisance

  • we now can digest case p=1, k>1 for asymmetric biastypes as well as for total variation
  • implemented lower Case solution for *=v p=1 k>1
  • roptest gains arguments withUpdateInKer, IC.UpdateInKer, na.rm

*** others

  • added argument fsCor to function roptest enabling a finite-sample correction of the radius ...
  • added QQ plots in examples to roptest

SCRIPTS

  • all scripts do run now without (obvious) error --- at the exception of NormalLocationScaleModel.R --- and there the radiusminimax solution for self-standardization ...
  • in script GammaModel.R, added comment due to new E method in distrEx which increases precision of certain computations.
  • scripts in part now with R output in comment
  • new example with k=15 steps in script PoissonModel.R
  • example for lower Case solution for *=v p=1 k>1 added in script NormalLocationScaleModel.R
  • new example for trafo-based model in script NormalLocationScaleModel.R
  • inserted some new lines in script NormalLocationScaleModel.R --- now has an example with nuisance parameters

GENERAL ENHANCEMENTS:

  • added tests/Examples folder with file ROptEst-Ex.Rout.save to have some automatic testing

  • added TOBEDONE (sic!) files; in English (for possible collaborators)

  • added keyword robust and made some minor corrections ...

  • added/updated NEWS files, updated CITATION files using code by A. Zeileis

  • Rd-parsing:

    • patch for Brian Ripley's Re: [Rd] Warning: missing text for item ... in \describe?
    • fixed errors / warnings in .Rd files detected by parser 2 (c.f. [Rd] More intensive checking of R help files, Prof Brian Ripley, 09.01.2009 10:25)
  • svn-revision-tags

    • added in all DESCRIPTION files
    • added field "Encoding: latin1" to all DESCRIPTION files because substituting $LastChangedDate by svn would cause problems for packages built under Windows (German) local when checking under Linux.
  • removed pdf-file from version control - Rnw-file is sufficient

INTERNALLY:

  • k dimension / p dimension -- trafo & nuisance

    • lower case and Hampel now seem to work with trafo
    • in getInfRob_asHampel: added argument checkBounds, setting this to FALSE clearly speeds up computations for asHampel Risk
    • cniper contamination now also available for partial ICs
    • slightly modified b search range in MSE problem -- in the hope it will do for Totalvariation neighborhood, p=1, k>1
    • new: getAsRisk for "asBias", "RealRandVariable", "TotalVarNeighborhood" and "ANY"
    • getModifyIC has been changed so that also nuisance parameter models can be covered.
  • new IC algorithm

    • upper by default is now set to NULL in getInfRobIC_asGRisk, getInfRobIC_asHampel, getIneffDiff
    • slightly modified b search range in MSE problem -- in the hope it will do for Totalvariation neighborhood, p=1, k>1
    • outsourced several steps in getInfRob_asGRisk.R and getInfRob_asHampel.R
      into internal, non-exported functions .getLowUpB() .getLowerSol() .getUpperSol() .checkUpLow()
    • radiusMinimaxIC gains argument loRad0 to be able to adjust the lower search bound (for getIneffDiff) case by case.
    • getInfCent, getInfGamma
      • uses getLow/getUp now
      • changed search interval for getInfCent Totalvariation one-dim
      • use of lower.tail = FALSE instead of 1-p in
    • verbosity:
      • for rob.-opt. ICs: in verbose mode now an automatic check for [p]IC is done
      • optIC, getIneffDiff, getInfLM, getInfRob, leastFavorableRadius, .LowerCaseMultivariate.R[TV], radiusMinimaxIC gain default NULL for argument verbose in these function we check for is.null and if so set it to getRobAStBaseOption("all.verbose")
      • new helper function .checkPIC for checking within getInfRobIC
      • work on pretty printing if verbose == TRUE, ...
      • getIneffDiff now inhibits permanent checks for IC even if verbose==TRUE
      • in addition to precision information, current Lagrange multipliers are issued if verbose==TRUE (but only every 5 iterations in asGRisk- and every 15 in asBias-method for getInfRobIC)
    • lowerCase solutions now count the number of iterations
    • changed detault search interval for r in radiusMinimaxIC.R
    • changed default search interval for b in getInfRobIC_asGRisk (one-dim)
    • getLagrangeMultBy... gain arg a.start to transmit the actual centering / clipping modification in transformed models
  • Risk slot

    • made Risk slot slightly more consistent (no longer double asMSE), in particular in case there is no convergence.
  • roptest

    • now has an argument initial.est.ArgList to transmit arguments for a call to initial.est (for those familiar with it: similarly to startEstArgList in roptest.gpareto...)
    • roptest gains arguments withUpdateInKer, IC.UpdateInKer, na.rm
  • getmodifyIC

    • new generic scaleUpdateIC for scale-Update in location/scale/locscale models -> to avoid similar code for the many variants ScaleModel, LocationScaleModel, LocationUnknownScaleModel, ScaleUnknownLocationModel; in the latter two also totalvariation nbds are allowed
    • getModifyIC gains ... argument and for signature((L2FamIC = "L2ParamFamily", neighbor = "Neighborhood", risk ="asRisk") inserts a verbose= getRobAStBaseOption("all.verbose") into modifyIC-slot

BUGFIXES:

  • scripts

    • two minor buglets in scripts NormalLocationScaleModel.R & UnderOverShootRisk.R
    • small shape parameters in GammaModel.R lead to functions which are hard to integrate numerically; added some code to demonstrate this ...
  • k dimension / p dimension issues

    • fixed issues with polymorph nature of slot param of ParamFamParameter: now we can determine opt-rob ICs for trafos; annotation gets right; see example(comparePlot)
    • Symmetry slots did not work correctly for non-trivial trafos (at least would have to be reworked); now: all entries are computed
    • in ..asHampel: bmax had to be converted to matrix in case p=1, k>1
  • new IC algorithm issues

    • in MSE-method (as iter <= 1 always), clipping bounds in weights in Total Variation case (p=1, k>1) were never updated -> new helper functino .isVirginW
    • small bugs removed in getInfRobIC_asGRisk, getInfRobIC_asHampel, getInfClip
    • std (standardization in non-standard norms) was not updated correctly in getLagrangeMultBy[...]
  • roptest

    • modifies slot start of return value to become initial.est argument
  • others:

    • definition of weight was missing in getInfRobIC_asCov.R
    • small bug in getAsRisk. Now radiusMinimaxIC works for models with trafo.
    • corrected a simple bug in scaleUpdateIC for UncondNeighborhoods
    • fixed an error in getModifyIC in the computation of the transferred risks
    • fixed a buglet in getModifyIC.R: had to cast out a second appearance of argument verbose (within ...) ...
    • getAsRisk for "asBias", "RealRandVariable", "ContNeighborhood" and "ANY" was lacking argument Finfo and did not check for verbose
    • minor documentation bug in radiusMinimaxIC.Rd

TO BE CHECKED

  • remains to be done: self standardization does not yet work...
  • total variation nbd: case 1=p<k works but still some checking needed.
  • to be checked: symm for total variation

####################################### version 0.6.2 #######################################

  • added functions to compute and plot cniper contamination and cniper points, respectively.
  • introduced option("newDevice") to control new opening of graphic devices
  • use of on.exit() to restore old settings for options() and par() at the end of functions
  • introduction of NEWS-file
  • update of CITATION-file (based on code provided by A. Zeileis on R help)

Reference manual

It appears you don't have a PDF plugin for this browser. You can click here to download the reference manual.

install.packages("ROptEst")

1.2.1 by Matthias Kohl, a month ago


http://robast.r-forge.r-project.org/


Browse source code at https://github.com/cran/ROptEst


Authors: Matthias Kohl [cre, cph] , Mykhailo Pupashenko [ctb] (contributed wrapper functions for diagnostic plots) , Gerald Kroisandt [ctb] (contributed testing routines) , Peter Ruckdeschel [aut, cph]


Documentation:   PDF Manual  


Task views: Robust Statistical Methods


LGPL-3 license


Imports startupmsg, MASS, stats, graphics, utils, grDevices

Depends on methods, distr, distrEx, distrMod, RandVar, RobAStBase

Suggests RobLox


Depended on by RobExtremes.

Suggested by RobAStBase.


See at CRAN