paep {AEP} | R Documentation |
Computes the cdf of AEP distribution given by
F_{X}(x|\Theta)=
\frac{1-\epsilon}{2}-\frac{1-\epsilon}{2 \Gamma\bigl(1+\frac{1}{\alpha}\bigr)} \gamma\Bigl(\Big|\frac{\mu-x}{\sigma(1-\epsilon)}\Big|^{\alpha},\frac{1}{\alpha}\Bigr),~{}~x < \mu,
F_{X}(x|\Theta)=
\frac{1-\epsilon}{2}+\frac{1+\epsilon}{2 \Gamma\bigl(1+\frac{1}{\alpha}\bigr)} \gamma\Bigl(\Big|\frac{x-\mu}{\sigma(1+\epsilon)}\Big|^{\alpha},\frac{1}{\alpha}\Bigr),~{{}}~x \geq \mu,
where -\infty<x<+\infty
, \Theta=(\alpha,\sigma,\mu,\epsilon)^T
with 0<\alpha \leq 2
, \sigma> 0
, -\infty<\mu<\infty
, and -1<\epsilon<1
.
paep(x, alpha, sigma, mu, epsilon, log.p = FALSE, lower.tail = TRUE)
x |
Vector of observations. |
alpha |
Tail thickness parameter. |
sigma |
Scale parameter. |
mu |
Location parameter. |
epsilon |
Skewness parameter. |
log.p |
If |
lower.tail |
If |
Computed cdf of AEP distribution at points of vector x
.
Mahdi Teimouri
paep(x = 2, alpha = 1.5, sigma = 1, mu = 0, epsilon = 0.5, log.p = FALSE, lower.tail = TRUE)