dpgnorm

The function evaluates the density $f(x,p,mean,sigma)$ of the univariate $p$-generalized normal distribution according to $$f(x,p,mean,\sigma)=(\sigma_p/ \sigma) \, C_p \, \exp \left( - \left( \frac{\sigma_p}{\sigma } \right)^p \frac{\left| x-mean \right|^p}{p} \right) ,$$ where $C_p=p^{1-1/p}/2/\Gamma(1/p)$ and $\sigma_p^2=p^{2/p} \, \Gamma(3/p)/ \Gamma(1/p)$.

distribution

Evaluation of the pdf and the cdf of the univariate,
noncentral, p-generalized normal distribution. Sampling from
the univariate, noncentral, p-generalized normal distribution
using either the p-generalized polar method, the p-generalized
rejecting polar method, the Monty Python method, the Ziggurat
method or the method of Nardon and Pianca. The package also
includes routines for the simulation of the bivariate,
p-generalized uniform distribution and the simulation of the
corresponding angular distribution.

Steve Kalke

pgnorm

The p-Generalized Normal Distribution

dpgnorm function

<dl><dt>y</dt>
<dd>The real argument of the function.</dd><dt>p</dt>
<dd>A positive number expressing the form parameter of the distribution. The default is 2.</dd><dt>mean</dt>
<dd>A real number expressing the expectation of the distribution. The default is 0.</dd><dt>sigma</dt>
<dd>A positive number expressing the standard deviation of the distribution. The default is $\sigma_p$.</dd></dl>

Arguments

Author

A function to evaluate the $p$-generalized normal density — dpgnorm

<dl>

<dt>y</dt>
<dd>The real argument of the function.</dd>

<dt>p</dt>
<dd>A positive number expressing the form parameter of the distribution. The default is 2.</dd>

<dt>mean</dt>
<dd>A real number expressing the expectation of the distribution. The default is 0.</dd>

<dt>sigma</dt>
<dd>A positive number expressing the standard deviation of the distribution. The default is $\sigma_p$.</dd>

</dl>

dpgnorm: A function to evaluate the \(p\)-generalized normal density

Description

Usage

Value

Arguments

Author

References

Examples