powdist (version 0.1.4)

PowerExponentialPower: 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 \(P[X \le x ]\), otherwise, P[X > x].

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 Baz<U+00E1>n J.L.

Examples

# NOT RUN {
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)
# }