Density, distribution function, quantile function, and random generation
for the left and/or right truncated student-t distribution with df
degrees of freedom.
dtt(x, location = 0, scale = 1, df, left = -Inf, right = Inf, log = FALSE)ptt(q, location = 0, scale = 1, df, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
rtt(n, location = 0, scale = 1, df, left = -Inf, right = Inf)
qtt(p, location = 0, scale = 1, df, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
dtt gives the density, ptt gives the distribution
function, qtt gives the quantile function, and rtt
generates random deviates.
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length is
taken to be the number required.
location parameter.
scale parameter.
degrees of freedom (> 0, maybe non-integer). df = Inf is
allowed.
left censoring point.
right censoring point.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
If location or scale are not specified they assume the default values
of 0 and 1, respectively. left and right have the defaults -Inf and Inf respectively.
The truncated student-t distribution has density $$f(x) = 1/\sigma \tau((x - \mu)/\sigma) / (T((right - \mu)/\sigma) - T((left - \mu)/\sigma))$$ for \(left \le x \le right\), and 0 otherwise.
where \(T\) and \(\tau\) are the cumulative distribution function
and probability density function of the student-t distribution with
df degrees of freedom respectively, \(\mu\) is the location of the
distribution, and \(\sigma\) the scale.