PowerExponentialPower {powdist} | R Documentation |
The Power Exponential Power Distribution
Description
Density, distribution function, quantile function and random generation for the power exponential power distribution with parameters mu, sigma, lambda and k.
Usage
dpexpow(x, lambda = 1, mu = 0, sigma = 1, k = 0, log = FALSE)
ppexpow(q, lambda = 1, mu = 0, sigma = 1, k = 0, lower.tail = TRUE,
log.p = FALSE)
qpexpow(p, lambda = 1, mu = 0, sigma = 1, k = 0, lower.tail = TRUE,
log.p = FALSE)
rpexpow(n, lambda = 1, mu = 0, sigma = 1, k = 0)
Arguments
x , q |
vector of quantiles. |
mu , sigma |
location and scale parameters. |
k , lambda |
shape parameters. |
log , log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are |
p |
vector of probabilities. |
n |
number of observations. |
Details
The power exponential power distribution has density
f\left(x\right)=\frac{\lambda}{\sigma}\left[\frac{e^{-\left(\frac{x-\mu}{\sigma}\right)}}{\left(1+e^{-\left(\frac{x-\mu}{\sigma}\right)}\right)^{2}}\right]\left[\frac{e^{\left(\frac{x-\mu}{\sigma}\right)}}{1+e^{\left(\frac{x-\mu}{\sigma}\right)}}\right]^{\lambda-1}
,
where -\infty<\mu<\infty
is the location paramether, \sigma^2>0
the scale parameter and \lambda>0
and k the shape parameters.
References
Lemonte A. and Bazán J.L.
Examples
dpexpow(1, 1, 3, 4, 1)
ppexpow(1, 1, 3, 4, 1)
qpexpow(0.2, 1, 3, 4, 1)
rpexpow(5, 2, 3, 4, 1)