Box–Cox t distribution (BCT)
bct.Rd
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)
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
Value
dbct
gives the density, pbct
gives the distribution function, qbct
gives the quantile function, and rbct
generates random deviates.
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.