The pasubbo returns the Cumulative Distribution Function at point x
for the AEP distribution with parameters \(a*\), \(b*\), \(m\).
pasubbo(x, m = 0, al = 1, ar = 1, bl = 2, br = 2)a vector containing the values for the probabilities.
(numeric) - value in the range \((-\infty, \infty)\) to evaluate the density.
(numeric) - location parameter.
(numeric) - scale parameters. Must be in the range \((0, \infty)\).
(numeric) - shape parameters. Must be in the range \((0, \infty)\).
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.