bcpe: Box-Cox Power Exponential distribution (BCPE)

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Box-Cox Power Exponential distribution (BCPE)

Description

Density, distribution function, quantile function, and random generation for the Box-Cox Power Exponential distribution.

Usage

dbcpe(x, mu = 5, sigma = 0.1, nu = 1, tau = 2, log = FALSE)

pbcpe(q, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)

qbcpe(p, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)

rbcpe(n, mu = 5, sigma = 0.1, nu = 1, tau = 2)

Arguments

x, q	vector of quantiles
mu	location parameter, must be positive.
sigma	scale parameter, must be positive.
nu	vector of nu parameter values.
tau	vector of tau parameter values, must be positive.
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

dbcpe and pbcpe allow for automatic differentiation with RTMB. The parameterisation follows the BCPE family of the gamlss.dist package.

The density is

f(x; \mu, \sigma, \nu, \tau) = \frac{x^{\nu-1}}{\mu^{\nu} \sigma} \frac{f_T(z;\tau)}{F_T\!\left(1/(\sigma|\nu|);\tau\right)}, \quad x > 0,

where z = [(x/\mu)^\nu - 1]/(\nu\sigma) for \nu \neq 0 and z = \log(x/\mu)/\sigma for \nu = 0, and f_T(\cdot;\tau) and F_T(\cdot;\tau) are the PDF and CDF of the power exponential (PE) distribution with shape \tau.

Value

dbcpe gives the density, pbcpe gives the distribution function, qbcpe gives the quantile function, and rbcpe generates random deviates.

References

Rigby, R. A. and Stasinopoulos, D. M. (2004) Smooth centile curves for skew and kurtotic data modelled using the Box-Cox Power Exponential distribution. Statistics in Medicine, 23, 3053-3076.

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/.

See Also

bccg, bct, powerexp

Examples

x <- rbcpe(1, mu = 5, sigma = 0.1, nu = 1, tau = 1)
d <- dbcpe(x, mu = 5, sigma = 0.1, nu = 1, tau = 1)
p <- pbcpe(x, mu = 5, sigma = 0.1, nu = 1, tau = 1)
q <- qbcpe(p, mu = 5, sigma = 0.1, nu = 1, tau = 1)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.