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. Probably the most important 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.

Author
Georg M. Goerg <im@gmge.org>
Date of publication
2016-03-29 10:48:16
Maintainer
Georg M. Goerg <im@gmge.org>
License
GPL (>= 2)
Version
0.6.4
URLs

View on CRAN

Man pages

analyze_convergence
Analyze convergence of Lambert W estimators
beta-utils
Utilities for parameter vector beta of the input distribution
bootstrap
Bootstrap Lambert W x F estimates
common-arguments
Common arguments for several functions
datasets
Datasets
delta_01
Input parameters to get zero mean, unit variance output given...
delta_GMM
Estimate delta
delta_Taylor
Estimate of delta by Taylor approximation
deprecated-functions
List of deprecated functions
distname-utils
Utilities for distributions supported in this package
estimate-moments
Skewness and kurtosis
gamma_01
Input parameters to get a zero mean, unit variance output for...
gamma_GMM
Estimate gamma
gamma_Taylor
Estimate gamma by Taylor approximation
Gaussianize
Gaussianize matrix-like objects
G_delta_alpha
Heavy tail transformation for Lambert W random variables
get_gamma_bounds
Get bounds for gamma
get_input
Back-transform Y to X
get_output
Transform input X to output Y
get_support
Computes support for skewed Lambert W x F distributions
H_gamma
H transformation with gamma
IGMM
Iterative Generalized Method of Moments - IGMM
ks.test.t
One-sample Kolmogorov-Smirnov test for student-t distribution
LambertW_fit-methods
Methods for Lambert W\times F estimates
LambertW_input_output-methods
Methods for Lambert W input and output objects
LambertW-package
R package for Lambert W \times F distributions
LambertW-toolkit
Do-it-yourself toolkit for Lambert W \times F distribution
LambertW-utils
Utilities for Lambert W \times F Random Variables
loglik-LambertW-utils
Log-Likelihood for Lambert W\times F RVs
lp_norm
lp norm of a vector
medcouple_estimator
MedCouple Estimator
MLE_LambertW
Maximum Likelihood Estimation for Lambert W \times F...
p_m1
Non-principal branch probability
tau-utils
Utilities for transformation vector tau
test_normality
Visual and statistical Gaussianity check
test_symmetry
Test symmetry based on Lambert W heavy tail(s)
theta-utils
Utilities for the parameter vector of Lambert W\times F...
U-utils
Zero-mean, unit-variance version of standard distributions
W
Lambert W function, its logarithm and derivative
W_delta
Inverse transformation for heavy-tail Lambert W RVs
W_gamma
Inverse transformation for skewed Lambert W RVs
xexp
Transformation that defines the Lambert W function and its...

Files in this package

LambertW
LambertW/inst
LambertW/inst/CITATION
LambertW/inst/include
LambertW/inst/include/LambertW_RcppExports.h
LambertW/inst/include/LambertW.h
LambertW/tests
LambertW/tests/testthat.R
LambertW/tests/testthat
LambertW/tests/testthat/test_aaa.R
LambertW/tests/testthat/test_lp_norm.R
LambertW/tests/testthat/test_dpqr_U.R
LambertW/tests/testthat/test_beta-utils.R
LambertW/tests/testthat/test_get_distname_family.R
LambertW/tests/testthat/test_distname-utils.R
LambertW/tests/testthat/test_W.R
LambertW/tests/testthat/test_theta-utils.R
LambertW/tests/testthat/test_get_support.R
LambertW/tests/testthat/test_H_gamma.R
LambertW/tests/testthat/test_estimate-moments.R
LambertW/tests/testthat/test_IGMM.R
LambertW/tests/testthat/test_deriv_W.R
LambertW/tests/testthat/test_LambertW_fit_methods.R
LambertW/tests/testthat/test_delta_01.R
LambertW/tests/testthat/test_loglik-utils.R
LambertW/tests/testthat/test_normalize_by_tau.R
LambertW/tests/testthat/test_dpqr_LambertW.R
LambertW/tests/testthat/test_p_m1.R
LambertW/tests/testthat/test_log_W.R
LambertW/tests/testthat/test_Gaussianize.R
LambertW/tests/testthat/test_MLE_LambertW.R
LambertW/tests/testthat/test_bootstrap.R
LambertW/tests/testthat/test_theta_tau.R
LambertW/tests/testthat/test_W_gamma.R
LambertW/tests/testthat/test_get_input_output.R
LambertW/tests/testthat/test_G_delta.R
LambertW/tests/testthat/test_W_delta.R
LambertW/tests/testthat/test_xexp.R
LambertW/tests/testthat/test_analyze_convergence.R
LambertW/src
LambertW/src/lp_norm_Cpp.cpp
LambertW/src/W_gamma_Cpp.cpp
LambertW/src/normalize_by_tau_Cpp.cpp
LambertW/src/W_Cpp.cpp
LambertW/src/W_delta_Cpp.cpp
LambertW/src/kurtosis.cpp
LambertW/src/RcppExports.cpp
LambertW/src/skewness.cpp
LambertW/NAMESPACE
LambertW/NEWS
LambertW/data
LambertW/data/SolarFlares.rda
LambertW/data/AA.rda
LambertW/R
LambertW/R/dLambertW.R
LambertW/R/deriv_W_delta.R
LambertW/R/0_LambertW_fit-methods.R
LambertW/R/loglik_LambertW.R
LambertW/R/test_symmetry.R
LambertW/R/tau2type.R
LambertW/R/0_LambertW-toolkit.R
LambertW/R/IGMM.R
LambertW/R/G_delta_alpha.R
LambertW/R/gamma_GMM.R
LambertW/R/0_tau-utils.R
LambertW/R/qU.R
LambertW/R/0_U-utils.R
LambertW/R/bootstrap.R
LambertW/R/p_m1.R
LambertW/R/complete_theta.R
LambertW/R/0_W.R
LambertW/R/gamma_01.R
LambertW/R/ks.test.t.R
LambertW/R/plot.LambertW_input.R
LambertW/R/pU.R
LambertW/R/xexp.R
LambertW/R/mLambertW.R
LambertW/R/create_LambertW_input.R
LambertW/R/print.LambertW_fit.R
LambertW/R/tau2theta.R
LambertW/R/rU.R
LambertW/R/unflatten_theta.R
LambertW/R/0_LambertW-utils.R
LambertW/R/common-arguments.R
LambertW/R/loglik_penalty.R
LambertW/R/normalize_by_tau.R
LambertW/R/medcouple_estimator.R
LambertW/R/get_distnames.R
LambertW/R/flatten_theta.R
LambertW/R/check_beta.R
LambertW/R/estimate_beta.R
LambertW/R/MLE_LambertW.R
LambertW/R/analyze_convergence.R
LambertW/R/plot.LambertW_fit.R
LambertW/R/test_normality.R
LambertW/R/theta2unbounded.R
LambertW/R/log_W.R
LambertW/R/check_theta.R
LambertW/R/0_beta-utils.R
LambertW/R/H_gamma.R
LambertW/R/get_input.R
LambertW/R/get_beta_names.R
LambertW/R/loglik_input.R
LambertW/R/get_support.R
LambertW/R/0_distname-utils.R
LambertW/R/qqLambertW.R
LambertW/R/complete_tau.R
LambertW/R/0_theta-utils.R
LambertW/R/print.summary.LambertW_fit.R
LambertW/R/deprecated_functions.R
LambertW/R/0_W_delta.R
LambertW/R/create_LambertW_output.R
LambertW/R/RcppExports.R
LambertW/R/deriv_W.R
LambertW/R/check_distname.R
LambertW/R/private_functions.R
LambertW/R/LambertW-package.R
LambertW/R/0_W_gamma.R
LambertW/R/rLambertW.R
LambertW/R/get_gamma_bounds.R
LambertW/R/lp_norm.R
LambertW/R/delta_01.R
LambertW/R/0_loglik-LambertW-utils.R
LambertW/R/beta2tau.R
LambertW/R/Gaussianize.R
LambertW/R/qLambertW.R
LambertW/R/get_initial_theta.R
LambertW/R/get_theta_bounds.R
LambertW/R/gamma_Taylor.R
LambertW/R/print.LambertW_output.R
LambertW/R/plot.LambertW_output.R
LambertW/R/summary.LambertW_fit.R
LambertW/R/delta_GMM.R
LambertW/R/get_initial_tau.R
LambertW/R/deriv_W_gamma.R
LambertW/R/datasets.R
LambertW/R/get_output.R
LambertW/R/delta_Taylor.R
LambertW/R/theta2tau.R
LambertW/R/zzz.R
LambertW/R/dU.R
LambertW/R/get_distname_family.R
LambertW/R/pLambertW.R
LambertW/R/print.LambertW_input.R
LambertW/R/check_tau.R
LambertW/R/0_LambertW_input_output-methods.R
LambertW/MD5
LambertW/DESCRIPTION
LambertW/man
LambertW/man/MLE_LambertW.Rd
LambertW/man/U-utils.Rd
LambertW/man/LambertW-package.Rd
LambertW/man/analyze_convergence.Rd
LambertW/man/LambertW_input_output-methods.Rd
LambertW/man/bootstrap.Rd
LambertW/man/get_gamma_bounds.Rd
LambertW/man/W.Rd
LambertW/man/distname-utils.Rd
LambertW/man/datasets.Rd
LambertW/man/LambertW-utils.Rd
LambertW/man/lp_norm.Rd
LambertW/man/beta-utils.Rd
LambertW/man/H_gamma.Rd
LambertW/man/IGMM.Rd
LambertW/man/LambertW-toolkit.Rd
LambertW/man/common-arguments.Rd
LambertW/man/ks.test.t.Rd
LambertW/man/medcouple_estimator.Rd
LambertW/man/W_delta.Rd
LambertW/man/xexp.Rd
LambertW/man/theta-utils.Rd
LambertW/man/deprecated-functions.Rd
LambertW/man/Gaussianize.Rd
LambertW/man/delta_Taylor.Rd
LambertW/man/gamma_GMM.Rd
LambertW/man/tau-utils.Rd
LambertW/man/get_support.Rd
LambertW/man/estimate-moments.Rd
LambertW/man/G_delta_alpha.Rd
LambertW/man/gamma_Taylor.Rd
LambertW/man/W_gamma.Rd
LambertW/man/get_input.Rd
LambertW/man/get_output.Rd
LambertW/man/delta_GMM.Rd
LambertW/man/LambertW_fit-methods.Rd
LambertW/man/delta_01.Rd
LambertW/man/gamma_01.Rd
LambertW/man/p_m1.Rd
LambertW/man/test_normality.Rd
LambertW/man/loglik-LambertW-utils.Rd
LambertW/man/test_symmetry.Rd