If mu
, sigmap
or p
are not specified they assume the default values 0, 1 and 2,
respectively.
The exponential power distribution has density function
$$f(x) = \frac{1}{2 p^{(1/p)} \Gamma(1+1/p) \sigma_p} e^{-\frac{|x - \mu|^p}{p \sigma_p^p}}$$
where \(\mu\) is the location parameter, \(\sigma_p\) the scale parameter and \(p\) the
shape parameter.
When \(p=2\) the exponential power distribution becomes the Normal Distribution, when
\(p=1\) the exponential power distribution becomes the Laplace Distribution, when
\(p\rightarrow\infty\) the exponential power distribution becomes the Uniform Distribution.