RTMBdist (version 0.1.0)

powerexp: Power Exponential distribution (PE and PE2)

Description

Density, distribution function, quantile function, and random generation for the Power Exponential distribution (two versions).

Usage

dpowerexp(x, mu = 0, sigma = 1, nu = 2, log = FALSE)
ppowerexp(q, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
qpowerexp(p, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
rpowerexp(n, mu = 0, sigma = 1, nu = 2)
dpowerexp2(x, mu = 0, sigma = 1, nu = 2, log = FALSE)
ppowerexp2(q, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
qpowerexp2(p, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
rpowerexp2(n, mu = 0, sigma = 1, nu = 2)

Value

dpowerexp gives the density, ppowerexp gives the distribution function, qpowerexp gives the quantile function, and rpowerexp generates random deviates.

Arguments

x, q

vector of quantiles

mu

location parameter

sigma

scale parameter, must be positive

nu

shape parameter (real)

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned 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 random values to return

Details

This implementation of the densities and distribution functions allow for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package.

For powerexp, mu is the mean and sigma is the standard deviation while this does not hold for powerexp2.

See gamlss.dist::PE for more details.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

# PE
x <- rpowerexp(1, mu = 0, sigma = 1, nu = 2)
d <- dpowerexp(x, mu = 0, sigma = 1, nu = 2)
p <- ppowerexp(x, mu = 0, sigma = 1, nu = 2)
q <- qpowerexp(p, mu = 0, sigma = 1, nu = 2)

# PE2
x <- rpowerexp2(1, mu = 0, sigma = 1, nu = 2)
d <- dpowerexp2(x, mu = 0, sigma = 1, nu = 2)
p <- ppowerexp2(x, mu = 0, sigma = 1, nu = 2)
q <- qpowerexp2(p, mu = 0, sigma = 1, nu = 2)