Skewed students t distribution
skewt.RdDensity, distribution function, quantile function, and random generation for the skew t distribution (type 2).
Usage
dskewt(x, mu = 0, sigma = 1, skew = 0, df = 1000, log = FALSE)
pskewt(q, mu = 0, sigma = 1, skew = 0, df = 1000,
method = 0, lower.tail = TRUE, log.p = FALSE)
qskewt(p, mu = 0, sigma = 1, skew = 0, df = 1000,
tol = 1e-8, method = 0)
rskewt(n, mu = 0, sigma = 1, skew = 0, df = 1000)Arguments
- x, q
vector of quantiles
- mu
location parameter
- sigma
scale parameter, must be positive.
- skew
skewness parameter, can be positive or negative.
- df
degrees of freedom, must be positive.
- log, log.p
logical; if
TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).- method
an integer value between 0 and 5 which selects the computing method; see ‘Details’ in the
pstdocumentation below for the meaning of these values. If method=0 (default value), an automatic choice is made among the four actual computing methods, depending on the other arguments.- lower.tail
logical; if
TRUE, probabilities are \(P[X <= x]\), otherwise, \(P[X > x]\).- p
vector of probabilities
- tol
a scalar value which regulates the accuracy of the result of qsn, measured on the probability scale.
- n
number of random values to return.
Value
dskewt gives the density, pskewt gives the distribution function, qskewt gives the quantile function, and rskewt generates random deviates.
Details
This corresponds to the skew t type 2 distribution in GAMLSS (ST2), see pp. 411-412 of Rigby et al. (2019) and the version implemented in the sn package.
This implementation of dskewt allows for automatic differentiation with RTMB while the other functions are imported from the sn package.
See sn::dst for more details.
Caution: In a numerial optimisation, the skew parameter should NEVER be initialised with exactly zero.
This will cause the initial and all subsequent derivatives to be exactly zero and hence the parameter will remain at its initial value.