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

## Documentation for package ‘LambertW’ version 0.6.9-2

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

A B C D E F G H I K L M N P Q R S T U V W X

## -- A --

AA | Datasets
analyze_convergence | Analyze convergence of Lambert W estimators

## -- B --

beta-utils | Utilities for parameter vector beta of the input distribution
beta2tau | Utilities for parameter vector beta of the input distribution
beta_names | List of deprecated functions
bootstrap | Bootstrap Lambert W x F estimates
bootstrap.LambertW_fit | Bootstrap Lambert W x F estimates
bounds_theta | List of deprecated functions

## -- C --

check_beta | Utilities for parameter vector beta of the input distribution
check_distname | Utilities for distributions supported in this package
check_tau | Utilities for transformation vector tau
check_theta | Utilities for the parameter vector of Lambert W\times F distributions
common-arguments | Common arguments for several functions
complete_tau | Utilities for transformation vector tau
complete_theta | Utilities for the parameter vector of Lambert W\times F distributions
create_LambertW_input | Do-it-yourself toolkit for Lambert W \times F distribution
create_LambertW_output | Do-it-yourself toolkit for Lambert W \times F distribution

## -- D --

d1W_1 | List of deprecated functions
datasets | Datasets
delta_01 | Input parameters to get zero mean, unit variance output given delta
delta_GMM | Estimate delta
delta_Taylor | Estimate of delta by Taylor approximation
deprecated-functions | List of deprecated functions
deriv_log_W | Lambert W function, its logarithm and derivative
deriv_W | Lambert W function, its logarithm and derivative
deriv_W_delta | Inverse transformation for heavy-tail Lambert W RVs
deriv_W_delta_alpha | Inverse transformation for heavy-tail Lambert W RVs
deriv_W_gamma | Inverse transformation for skewed Lambert W RVs
deriv_xexp | Transformation that defines the Lambert W function and its derivative
distname-utils | Utilities for distributions supported in this package
dLambertW | Utilities for Lambert W \times F Random Variables
dU | Zero-mean, unit-variance version of standard distributions

## -- E --

estimate_beta | Utilities for parameter vector beta of the input distribution

## -- F --

flatten_theta | Utilities for the parameter vector of Lambert W\times F distributions

## -- G --

gamma_01 | Input parameters to get a zero mean, unit variance output for a given gamma
gamma_GMM | Estimate gamma
gamma_Taylor | Estimate gamma by Taylor approximation
Gaussianize | Gaussianize matrix-like objects
get.input | Back-transform Y to X
get_beta_names | Utilities for parameter vector beta of the input distribution
get_distnames | Utilities for distributions supported in this package
get_distname_family | Utilities for distributions supported in this package
get_gamma_bounds | Get bounds for gamma
get_initial_tau | Utilities for transformation vector tau
get_initial_theta | Utilities for the parameter vector of Lambert W\times F distributions
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
get_theta_bounds | Utilities for the parameter vector of Lambert W\times F distributions
G_2delta_2alpha | Heavy tail transformation for Lambert W random variables
G_delta | Heavy tail transformation for Lambert W random variables
G_delta_alpha | Heavy tail transformation for Lambert W random variables

## -- H --

H | List of deprecated functions
H_gamma | H transformation with gamma

## -- I --

IGMM | Iterative Generalized Method of Moments - IGMM

## -- K --

ks_test_t | One-sample Kolmogorov-Smirnov test for student-t distribution
kurtosis | Skewness and kurtosis

## -- L --

LambertW-toolkit | Do-it-yourself toolkit for Lambert W \times F distribution
LambertW-utils | Utilities for Lambert W \times F Random Variables
LambertW_fit-methods | Methods for Lambert W\times F estimates
LambertW_input_output-methods | Methods for Lambert W input and output objects
loglik-LambertW-utils | Log-Likelihood for Lambert W\times F RVs
loglik_input | Log-Likelihood for Lambert W\times F RVs
loglik_LambertW | Log-Likelihood for Lambert W\times F RVs
loglik_penalty | Log-Likelihood for Lambert W\times F RVs
log_deriv_W | Lambert W function, its logarithm and derivative
log_W | Lambert W function, its logarithm and derivative
lp_norm | lp norm of a vector

## -- M --

medcouple_estimator | MedCouple Estimator
mLambertW | Utilities for Lambert W \times F Random Variables
MLE_LambertW | Maximum Likelihood Estimation for Lambert W \times F distributions

## -- N --

normalize_by_tau | Utilities for transformation vector tau
normfit | List of deprecated functions

## -- P --

params2theta | List of deprecated functions
pLambertW | Utilities for Lambert W \times F Random Variables
plot.convergence_LambertW_fit | Analyze convergence of Lambert W estimators
plot.LambertW_fit | Methods for Lambert W\times F estimates
plot.LambertW_input | Methods for Lambert W input and output objects
plot.LambertW_output | Methods for Lambert W input and output objects
print.LambertW_fit | Methods for Lambert W\times F estimates
print.LambertW_input | Methods for Lambert W input and output objects
print.LambertW_output | Methods for Lambert W input and output objects
print.summary.LambertW_fit | Methods for Lambert W\times F estimates
pU | Zero-mean, unit-variance version of standard distributions
p_1 | List of deprecated functions
p_m1 | Non-principal branch probability

## -- Q --

qLambertW | Utilities for Lambert W \times F Random Variables
qqLambertW | Utilities for Lambert W \times F Random Variables
qU | Zero-mean, unit-variance version of standard distributions

## -- R --

rLambertW | Utilities for Lambert W \times F Random Variables
rU | Zero-mean, unit-variance version of standard distributions

## -- S --

skewness | Skewness and kurtosis
skewness_test | List of deprecated functions
SolarFlares | Datasets
starting_theta | List of deprecated functions
summary.convergence_LambertW_fit | Analyze convergence of Lambert W estimators
summary.LambertW_fit | Methods for Lambert W\times F estimates
support | List of deprecated functions

## -- T --

tau-utils | Utilities for transformation vector tau
tau2theta | Utilities for transformation vector tau
tau2type | Utilities for transformation vector tau
test_norm | Visual and statistical Gaussianity check
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 distributions
theta2params | List of deprecated functions
theta2tau | Utilities for the parameter vector of Lambert W\times F distributions
theta2unbounded | Utilities for the parameter vector of Lambert W\times F distributions

## -- U --

U-utils | Zero-mean, unit-variance version of standard distributions
unflatten_theta | Utilities for the parameter vector of Lambert W\times F distributions

## -- V --

vec.norm | List of deprecated functions

## -- W --

W | Lambert W function, its logarithm and derivative
W_1 | List of deprecated functions
W_2delta | Inverse transformation for heavy-tail Lambert W RVs
W_2delta_2alpha | Inverse transformation for heavy-tail Lambert W RVs
W_delta | Inverse transformation for heavy-tail Lambert W RVs
W_delta_alpha | Inverse transformation for heavy-tail Lambert W RVs
W_gamma | Inverse transformation for skewed Lambert W RVs
W_gamma_1 | List of deprecated functions

## -- X --

xexp | Transformation that defines the Lambert W function and its derivative