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[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 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)

[Package powdist version 0.1.4 Index]