Density, distribution function, quantile function, and random generation for
the Box–Cox Cole and Green distribution.
Usage
dbccg(x, mu = 1, sigma = 0.1, nu = 1, log = FALSE)
pbccg(q, mu = 1, sigma = 0.1, nu = 1, lower.tail = TRUE, log.p = FALSE)
qbccg(p, mu = 1, sigma = 0.1, nu = 1, lower.tail = TRUE, log.p = FALSE)
rbccg(n, mu = 1, sigma = 0.1, nu = 1)
Value
dbccg gives the density, pbccg gives the distribution function, qbccg gives the quantile function, and rbccg 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).
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 dbccg and pbccg allows for automatic differentiation with RTMB while the other functions are imported from gamlss.dist package.
See gamlss.dist::BCCG 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/.
x <- rbccg(5, mu = 10, sigma = 0.2, nu = 0.5)
d <- dbccg(x, mu = 10, sigma = 0.2, nu = 0.5)
p <- pbccg(x, mu = 10, sigma = 0.2, nu = 0.5)
q <- qbccg(p, mu = 10, sigma = 0.2, nu = 0.5)