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Rsubbotools (version 0.0.1)

ppower: Returns CDF from EP Distribution

Description

The ppower returns the Cumulative Distribution Function at point x for the Exponential Power distribution with parameters \(a\), \(b\) and \(m\).

Usage

ppower(x, m = 0, a = 1, b = 2)

Value

a vector containing the values for the probabilities.

Arguments

x

(numeric) - value in the range \((-\infty, \infty)\) to evaluate the density.

m

(numeric) - location parameter. Must be in the range

a

(numeric) - scale parameter. Must be in the range \((0, \infty)\).

b

(numeric) - shape parameter. Must be in the range \((0, \infty)\). \((-\infty, \infty)\).

Details

The Exponential Power distribution (EP) is given by the function: $$ f(a,b) = \frac{1}{2a\Gamma(1+1/b)}e^{-|(x-m)/a|^b}, -\infty < x < \infty $$. where \(b\) is a shape parameter, \(a\) is a scale parameter, \(m\) is a location parameter and \(\Gamma\) represents the gamma function.