powdist (version 0.1.4)

PowerLaplace: The Power Laplace Distribution

Description

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

Usage

dplaplace(x, lambda = 1, mu = 0, sigma = 1, log = FALSE)
pplaplace(q, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)
qplaplace(p, lambda = 1, mu = 0, sigma = 1, lower.tail = TRUE,
  log.p = FALSE)
rplaplace(n, lambda = 1, mu = 0, sigma = 1)

Arguments

x, q

vector of quantiles.

lambda

shape parameter.

mu, sigma

location and scale 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 Laplace distribution has density

\(f(x)=\lambda\left[\frac{1}{2}+\frac{\left(1-e^{-\frac{\left|x-\mu\right|}{\sigma}}\right)}{2}\textrm{sign}\left(\frac{x-\mu}{\sigma}\right)\right]^{\lambda-1}\left[\frac{e^{-\frac{\left|x-\mu\right|}{\sigma}}}{2\sigma}\right]\), where \(-\infty<\mu<\infty\) is the location paramether, \(\sigma^2>0\) the scale parameter and \(\lambda>0\) the shape parameter.

Examples

# NOT RUN {
dplaplace(1, 1, 3, 4)
pplaplace(1, 1, 3, 4)
qplaplace(0.2, 1, 3, 4)
rplaplace(5, 2, 3, 4)
# }