qasubbo: Returns CDF from the AEP Distribution

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

Returns CDF from the AEP Distribution

Description

The qasubbo returns the density at point x for the AEP distribution with parameters a*, b*, m.

Usage

qasubbo(x, m = 0, al = 1, ar = 1, bl = 2, br = 2)

Arguments

x	(numeric) - value in the range (-\infty, \infty) to evaluate the density.
m	(numeric) - location parameter.
al, ar	(numeric) - scale parameters. Must be in the range (0, \infty).
bl, br	(numeric) - shape parameters. Must be in the range (0, \infty).

Details

The AEP is a exponential power distribution controlled by five parameters, with formula:

f(x;a_l,a_r,b_l,b_r,m) = \frac{1}{A} e^{- \frac{1}{b_l} |\frac{x-m}{a_l}|^{b_l} }, x < m

f(x;a_l,a_r,b_l,b_r,m) = \frac{1}{A} e^{- \frac{1}{b_r} |\frac{x-m}{a_r}|^{b_r} }, x > m

with:

A = a_lb_l^{1/b_l}\Gamma(1+1/b_l) + a_rb_r^{1/b_r}\Gamma(1+1/b_r)

where l and r represent left and right tails, a* are scale parameters, b* control the tails (lower values represent fatter tails), and m is a location parameter.

Value

a vector containing the values for the densities.

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