Package: LambertW 0.6.9-1

LambertW: Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data

Lambert W x F distributions are a generalized framework to analyze skewed, heavy-tailed data. It is based on an input/output system, where the output random variable (RV) Y is a non-linearly transformed version of an input RV X ~ F with similar properties as X, but slightly skewed (heavy-tailed). The transformed RV Y has a Lambert W x F distribution. This package contains functions to model and analyze skewed, heavy-tailed data the Lambert Way: simulate random samples, estimate parameters, compute quantiles, and plot/ print results nicely. The most useful function is 'Gaussianize', which works similarly to 'scale', but actually makes the data Gaussian. A do-it-yourself toolkit allows users to define their own Lambert W x 'MyFavoriteDistribution' and use it in their analysis right away.

Authors:Georg M. Goerg [aut, cre]

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NEWS

# Install 'LambertW' in R:
install.packages('LambertW', repos = c('https://gmgeorg.r-universe.dev', 'https://cloud.r-project.org'))

Peer review:

Bug tracker:https://github.com/gmgeorg/lambertw/issues

Uses libs:
  • c++– GNU Standard C++ Library v3
Datasets:

On CRAN:

gaussianizegaussianize-dataheavy-tailedheavy-tailed-distributionsleptokurtosisnormal-distributionnormalizationskewed-datastatistics

8.38 score 9 stars 12 packages 75 scripts 3.3k downloads 3 mentions 94 exports 35 dependencies

Last updated 11 months agofrom:592c342ad1. Checks:OK: 7 NOTE: 2. Indexed: yes.

TargetResultDate
Doc / VignettesOKOct 27 2024
R-4.5-win-x86_64NOTEOct 27 2024
R-4.5-linux-x86_64NOTEOct 27 2024
R-4.4-win-x86_64OKOct 27 2024
R-4.4-mac-x86_64OKOct 27 2024
R-4.4-mac-aarch64OKOct 27 2024
R-4.3-win-x86_64OKOct 27 2024
R-4.3-mac-x86_64OKOct 27 2024
R-4.3-mac-aarch64OKOct 27 2024

Exports:analyze_convergencebeta_namesbeta2taubootstrapbounds_thetacheck_betacheck_distnamecheck_taucheck_thetacomplete_taucomplete_thetacreate_LambertW_inputcreate_LambertW_outputd1W_1delta_01delta_GMMdelta_Taylorderiv_log_Wderiv_Wderiv_W_deltaderiv_W_delta_alphaderiv_W_gammaderiv_xexpdLambertWdUestimate_betaflatten_thetaG_2delta_2alphaG_deltaG_delta_alphagamma_01gamma_GMMgamma_TaylorGaussianizeget_beta_namesget_distname_familyget_distnamesget_gamma_boundsget_initial_tauget_initial_thetaget_inputget_outputget_supportget_theta_boundsget.inputHH_gammaIGMMks_test_tkurtosislog_deriv_Wlog_Wloglik_inputloglik_LambertWloglik_penaltylp_normmedcouple_estimatormLambertWMLE_LambertWnormalize_by_taunormfitp_1p_m1params2thetapLambertWpUqLambertWqqLambertWqUrLambertWrUskewnessskewness_teststarting_thetasupporttau2thetatau2typetest_normtest_normalitytest_symmetrytheta2paramstheta2tautheta2unboundedunflatten_thetavec.normWW_1W_2deltaW_2delta_2alphaW_deltaW_delta_alphaW_gammaW_gamma_1xexp

Dependencies:clicolorspacefansifarverggplot2gluegtableisobandlabelinglamWlatticelifecyclemagrittrMASSMatrixmgcvmunsellnlmepillarpkgconfigplyrR6RColorBrewerRcppRcppParallelreshape2rlangscalesstringistringrtibbleutf8vctrsviridisLitewithr

LambertW Overview

Rendered fromlambertw-overview.Rmdusingknitr::knitron Oct 27 2024.

Last update: 2023-09-02
Started: 2020-06-07

Readme and manuals

Help Manual

Help pageTopics
R package for Lambert W \times F distributionsLambertW-package LambertW
Analyze convergence of Lambert W estimatorsanalyze_convergence plot.convergence_LambertW_fit summary.convergence_LambertW_fit
Utilities for parameter vector beta of the input distributionbeta-utils beta2tau check_beta estimate_beta get_beta_names
Bootstrap Lambert W x F estimatesbootstrap bootstrap.LambertW_fit
Common arguments for several functionscommon-arguments
DatasetsAA datasets SolarFlares
Input parameters to get zero mean, unit variance output given deltadelta_01
Estimate deltadelta_GMM
Estimate of delta by Taylor approximationdelta_Taylor
List of deprecated functionsbeta_names bounds_theta d1W_1 deprecated-functions H normfit params2theta p_1 skewness_test starting_theta support theta2params vec.norm W_1 W_gamma_1
Utilities for distributions supported in this packagecheck_distname distname-utils get_distnames get_distname_family
Heavy tail transformation for Lambert W random variablesG_2delta_2alpha G_delta G_delta_alpha
Input parameters to get a zero mean, unit variance output for a given gammagamma_01
Estimate gammagamma_GMM
Estimate gamma by Taylor approximationgamma_Taylor
Gaussianize matrix-like objectsGaussianize
Get bounds for gammaget_gamma_bounds
Back-transform Y to Xget.input get_input
Transform input X to output Yget_output
Computes support for skewed Lambert W x F distributionsget_support
H transformation with gammaH_gamma
Iterative Generalized Method of Moments - IGMMIGMM
One-sample Kolmogorov-Smirnov test for student-t distributionks_test_t
Skewness and kurtosiskurtosis skewness
Methods for Lambert W\times F estimatesLambertW_fit-methods plot.LambertW_fit print.LambertW_fit print.summary.LambertW_fit summary.LambertW_fit
Methods for Lambert W input and output objectsLambertW_input_output-methods plot.LambertW_input plot.LambertW_output print.LambertW_input print.LambertW_output
Do-it-yourself toolkit for Lambert W \times F distributioncreate_LambertW_input create_LambertW_output LambertW-toolkit
Utilities for Lambert W \times F Random VariablesdLambertW LambertW-utils mLambertW pLambertW qLambertW qqLambertW rLambertW
Log-Likelihood for Lambert W\times F RVsloglik-LambertW-utils loglik_input loglik_LambertW loglik_penalty
lp norm of a vectorlp_norm
MedCouple Estimatormedcouple_estimator
Maximum Likelihood Estimation for Lambert W \times F distributionsMLE_LambertW
Non-principal branch probabilityp_m1
Utilities for transformation vector taucheck_tau complete_tau get_initial_tau normalize_by_tau tau-utils tau2theta tau2type
Visual and statistical Gaussianity checktest_norm test_normality
Test symmetry based on Lambert W heavy tail(s)test_symmetry
Utilities for the parameter vector of Lambert W\times F distributionscheck_theta complete_theta flatten_theta get_initial_theta get_theta_bounds theta-utils theta2tau theta2unbounded unflatten_theta
Zero-mean, unit-variance version of standard distributionsdU pU qU rU U-utils
Lambert W function, its logarithm and derivativederiv_log_W deriv_W log_deriv_W log_W W
Inverse transformation for heavy-tail Lambert W RVsderiv_W_delta deriv_W_delta_alpha W_2delta W_2delta_2alpha W_delta W_delta_alpha
Inverse transformation for skewed Lambert W RVsderiv_W_gamma W_gamma
Transformation that defines the Lambert W function and its derivativederiv_xexp xexp