powdist (version 0.1.4)

ExponentialPower: The Exponential Power Distribution

Description

Density, distribution function, quantile function and random generation for the exponential power distribution with parameters mu, sigma and k.

Usage

dexpow(x, mu = 0, sigma = 1, k = 0, log = FALSE)
pexpow(q, mu = 0, sigma = 1, k = 0, lower.tail = TRUE, log.p = FALSE)
qexpow(p, mu = 0, sigma = 1, k = 0, lower.tail = TRUE, log.p = FALSE)
rexpow(n, mu = 0, sigma = 1, k = 0)

Arguments

x, q

vector of quantiles.

mu, sigma

location and scale parameters.

k

shape parameter.

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 Exponential distribution has density

\(f\left(x\right)=\left[\frac{e^{-\left(\frac{x-\mu}{\sigma}\right)}}{\left(1+e^{-\left(\frac{x-\mu}{\sigma}\right)}\right)^{2}}\right]\),

where \(-\infty<\mu<\infty\) is the location paramether, \(\sigma^2>0\) the scale parameter and k the shape parameter.

References

Lemonte A. and Baz<U+00E1>n J.L.

Examples

# NOT RUN {
dexpow(1, 3, 4, 1)
pexpow(1, 3, 4, 1)
qexpow(0.2, 3, 4, 1)
rexpow(5, 3, 4, 1)
# }