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.

AuthorGeorg M. Goerg <im@gmge.org>
Date of publication2016-03-29 10:48:16
MaintainerGeorg M. Goerg <im@gmge.org>
LicenseGPL (>= 2)
Version0.6.4
http://www.gmge.org http://arxiv.org/abs/0912.4554 http://arxiv.org/abs/1010.2265 http://arxiv.org/abs/1602.02200

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...

Functions

AA Man page
analyze_convergence Man page
beta2tau Man page
beta_names Man page
beta-utils Man page
bootstrap Man page
bootstrap.LambertW_fit Man page
bounds_theta Man page
check_beta Man page
check_distname Man page
check_tau Man page
check_theta Man page
common-arguments Man page
complete_tau Man page
complete_theta Man page
create_LambertW_input Man page
create_LambertW_output Man page
d1W_1 Man page
datasets Man page
delta_01 Man page
delta_GMM Man page
delta_Taylor Man page
deprecated-functions Man page
deriv_log_W Man page
deriv_W Man page
deriv_W_delta Man page
deriv_W_delta_alpha Man page
deriv_W_gamma Man page
deriv_xexp Man page
distname-utils Man page
dLambertW Man page
dU Man page
estimate_beta Man page
flatten_theta Man page
G_2delta_2alpha Man page
gamma_01 Man page
gamma_GMM Man page
gamma_Taylor Man page
Gaussianize Man page
G_delta Man page
G_delta_alpha Man page
get_beta_names Man page
get_distname_family Man page
get_distnames Man page
get_gamma_bounds Man page
get_initial_tau Man page
get_initial_theta Man page
get_input Man page
get.input Man page
get_output Man page
get_support Man page
get_theta_bounds Man page
H Man page
H_gamma Man page
IGMM Man page
ks.test.t Man page
kurtosis Man page
LambertW Man page
LambertW_fit-methods Man page
LambertW_input_output-methods Man page
LambertW-package Man page
LambertW-toolkit Man page
LambertW-utils Man page
log_deriv_W Man page
loglik_input Man page
loglik_LambertW Man page
loglik-LambertW-utils Man page
loglik_penalty Man page
log_W Man page
lp_norm Man page
medcouple_estimator Man page
mLambertW Man page
MLE_LambertW Man page
normalize_by_tau Man page
normfit Man page
p_1 Man page
params2theta Man page
pLambertW Man page
plot.convergence_LambertW_fit Man page
plot.LambertW_fit Man page
plot.LambertW_input Man page
plot.LambertW_output Man page
p_m1 Man page
print.LambertW_fit Man page
print.LambertW_input Man page
print.LambertW_output Man page
print.summary.LambertW_fit Man page
pU Man page
qLambertW Man page
qqLambertW Man page
qU Man page
rLambertW Man page
rU Man page
skewness Man page
skewness_test Man page
SolarFlares Man page
starting_theta Man page
summary.convergence_LambertW_fit Man page
summary.LambertW_fit Man page
support Man page
tau2theta Man page
tau2type Man page
tau-utils Man page
test_norm Man page
test_normality Man page
test_symmetry Man page
theta2params Man page
theta2tau Man page
theta2unbounded Man page
theta-utils Man page
unflatten_theta Man page
U-utils Man page
vec.norm Man page
W Man page
W_1 Man page
W_2delta Man page
W_2delta_2alpha Man page
W_delta Man page
W_delta_alpha Man page
W_gamma Man page
W_gamma_1 Man page
xexp Man page

Files

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

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