RTMBdist (version 0.1.0)

bct: Box–Cox t distribution (BCT)

Description

Density, distribution function, quantile function, and random generation for the Box–Cox t distribution.

Usage

dbct(x, mu = 5, sigma = 0.1, nu = 1, tau = 2, log = FALSE)
pbct(q, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)
qbct(p, mu = 5, sigma = 0.1, nu = 1, tau = 2, lower.tail = TRUE, log.p = FALSE)
rbct(n, mu = 5, sigma = 0.1, nu = 1, tau = 2)

Value

dbct gives the density, pbct gives the distribution function, qbct gives the quantile function, and rbct generates random deviates.

Arguments

x, q

vector of quantiles

mu

location parameter, must be positive.

sigma

scale parameter, must be positive.

nu

skewness parameter (real).

tau

degrees of freedom, 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

This implementation of dbct and pbct allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package. See gamlss.dist::BCT 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

x <- rbct(1, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)
d <- dbct(x, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)
p <- pbct(x, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)
q <- qbct(p, mu = 10, sigma = 0.2, nu = 0.5, tau = 4)