psep: Returns CDF from the Skewed Exponential Power distribution

In Rsubbotools: Fast Estimation of Subbottin and AEP Distributions (Generalized Error Distribution)

Returns CDF from the Skewed Exponential Power distribution

Description

The psep returns the Cumulative Distribution Function at point x for the Skewed Exponential Power distribution with parameters a, b.

Usage

psep(x, m = 0, a = 2, b = 1, lambda = 0)

Arguments

x	vector with values to evaluate CDF.
m	the location parameter.
a	the scale parameter.
b	the shape parameter
lambda	the skewness parameter.

Details

The SEP is a exponential power distribution controlled by four parameters, with formula:

f(x; m, b, a, \lambda) = 2 \Phi(w) e^{-|z|^b/b}/(c)

where:

z = (x-m)/a

w = sign(z) |z|^{(b/2)} \lambda \sqrt{2/b}

c = 2 ab^{(1/b)-1} \Gamma(1/b)

with \Phi the cumulative normal distribution with mean zero and variance one. The CDF is calculated through numerical integration using the 'GSL' suite.

Value

a vector containing the values for the probabilities.

Rsubbotools documentation built on April 16, 2025, 5:10 p.m.