common-arguments

a numeric vector of real values (the observed data).

character; name of input distribution; see
<code><a rd-options="" href="/link/get_distnames?package=LambertW&version=0.6.4" data-mini-rdoc="LambertW::get_distnames">get_distnames</a></code>.

distname

type of Lambert W \(\times\) F distribution: skewed <code>"s"</code>;
heavy-tail <code>"h"</code>; or skewed heavy-tail <code>"hh"</code>.

type

list; a (possibly incomplete) list of parameters <code>alpha</code>,
<code>beta</code>, <code>gamma</code>, <code>delta</code>. <code><a rd-options="" href="/link/complete_theta?package=LambertW&version=0.6.4" data-mini-rdoc="LambertW::complete_theta">complete_theta</a></code>
fills in default values for missing entries.

theta

numeric vector (deprecated); parameter \(\boldsymbol \beta\) of
the input distribution. See <code><a rd-options="" href="/link/check_beta?package=LambertW&version=0.6.4" data-mini-rdoc="LambertW::check_beta">check_beta</a></code> on how to specify
<code>beta</code> for each distribution.

beta

scalar (deprecated); skewness parameter; default: <code>0</code>.

gamma

scalar or vector (length 2) (deprecated); heavy-tail
parameter(s); default: <code>0</code>.

delta

scalar or vector (length 2) (deprecated); heavy tail
exponent(s); default: <code>1</code>.

alpha

named vector \(\tau\) which defines the variable transformation.
Must have at least <code>'mu_x'</code> and <code>'sigma_x'</code> element; see
<code><a rd-options="" href="/link/complete_tau?package=LambertW&version=0.6.4" data-mini-rdoc="LambertW::complete_tau">complete_tau</a></code> for details.

logical; if <code>TRUE</code>, it returns the standardized input
that corresponds to \(U\), which is the zero-mean and/or unit-variance
version of input \(X \sim F_X\).

return.u

logical; if <code>TRUE</code> it uses mean and variance
implied by \(\boldsymbol \beta\) to do the transformation (Goerg 2011).
If <code>FALSE</code>, it uses the alternative definition from Goerg (2016)
with location and scale parameter.

use.mean.variance

Reference list of most common function arguments in this package.

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.

Georg M Goerg

LambertW

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

common-arguments function

character; name of input distribution; see
<code><a rd-options='' href='get_distnames'>get_distnames</a></code>.

list; a (possibly incomplete) list of parameters <code>alpha</code>,
<code>beta</code>, <code>gamma</code>, <code>delta</code>. <code><a rd-options='' href='complete_theta'>complete_theta</a></code>
fills in default values for missing entries.

numeric vector (deprecated); parameter \(\boldsymbol \beta\) of
the input distribution. See <code><a rd-options='' href='check_beta'>check_beta</a></code> on how to specify
<code>beta</code> for each distribution.

named vector \(\tau\) which defines the variable transformation.
Must have at least <code>'mu_x'</code> and <code>'sigma_x'</code> element; see
<code><a rd-options='' href='complete_tau'>complete_tau</a></code> for details.

common-arguments: Common arguments for several functions

Description

Arguments