lp_norm

Computes the $\ell^p$ norm of an n-dimensional (real/complex) 
vector $\mathbf{x} \in \mathbf{C}^n$
$$ \left|\left| \mathbf{x} \right|\right|_p = \left( \sum_{i=1}^n
\left| x_i \right|^p \right)^{1/p}, p \in [0, \infty],$$
where $\left| x_i \right|$ is the absolute value of $x_i$. For
 $p=2$ this is Euclidean norm; for $p=1$ it is Manhattan norm. For
 $p=0$ it is defined as the number of non-zero elements in
 $\mathbf{x}$; for $p = \infty$ it is the maximum of the absolute
 values of $\mathbf{x}$.
The norm of $\mathbf{x}$ equals $0$ if and only if $\mathbf{x} =
 \mathbf{0}$.

math

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. The most useful 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

Georg M. Goerg

lp_norm function

<dl><dt>x</dt>
<dd>n-dimensional vector (possibly complex values)</dd>
<dt>p</dt>
<dd>which norm? Allowed values $p \geq 0$ including <code>Inf</code>. 
Default: <code>2</code> (Euclidean norm).</dd></dl>

Arguments

lp norm of a vector — lp_norm

<dl>

<dt>x</dt>
<dd>n-dimensional vector (possibly complex values)</dd>


<dt>p</dt>
<dd>which norm? Allowed values $p \geq 0$ including <code>Inf</code>. 
Default: <code>2</code> (Euclidean norm).</dd>

</dl>

lp_norm: lp norm of a vector

Description

Usage

Value

Arguments

Examples