U-utils
(Package: LambertW) :
Zero-mean, unit-variance version of standard distributions
Density, distribution function, quantile function and random number generation for the shifted and scaled U of the (location-)scale family input X sim F_X(x mid oldsymbol β) - see References.
● Data Source:
CranContrib
● Keywords: datagen, distribution, univar
● Alias: U-utils, dU, pU, qU, rU
●
2 images
This package is based on notation, definitions, and results of Goerg (2011, 2015, 2016). I will not include these references in the description of each single function.
Analyzes the feasibility of a Lambert W x F distribution for a given dataset based on bootstrapping. In particular it checks whether parameter estimates support the hypothesis that the data indeed follows a Lambert W x F distribution with finite mean and variance of the input distribution, which is an implicit assumption of Lambert W x F random variables in Goerg (2011).
get_gamma_bounds returns lower and upper bounds for γ, so that the observed data range falls within the theoretical bounds of the support of the distribution. This is only important for location family input.
W
(Package: LambertW) :
Lambert W function, its logarithm and derivative
The Lambert W function W(z) = u is defined as the inverse of (see xexp)
● Data Source:
CranContrib
● Keywords: math
● Alias: W, deriv_W, deriv_log_W, log_W, log_deriv_W
●
2 images
distname-utils
(Package: LambertW) :
Utilities for distributions supported in this package
The Lambert W\times F framework can take any (continuous) random variable with distribution F and make it skewed (type = "s"), heavy tailed (type = "h"), or both (type = "hh").
Density, distribution, quantile function and random number generation for a Lambert W \timesF_X(x mid oldsymbol β) random variable with parameter θ = (α, oldsymbol β, γ, δ).
providing 
.