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)

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. If `length(n) > 1`

, the length is
taken to be the number required.

location

location parameter.

scale

scale parameter.

df

degrees of freedom (> 0, maybe non-integer). `df = Inf`

is
allowed.

left

left censoring point.

right

right censoring point.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].

`dtt`

gives the density, `ptt`

gives the distribution
function, `qtt`

gives the quantile function, and `rtt`

generates random deviates.

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.