The Truncated Student-t Distribution
Density, distribution function, quantile function, and random generation
for the left and/or right truncated student-t distribution with
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.
vector of probabilities.
number of observations. If
length(n) > 1, the length is taken to be the number required.
degrees of freedom (> 0, maybe non-integer).
df = Infis allowed.
left censoring point.
right censoring point.
- log, log.p
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
scale are not specified they assume the default values
right have the defaults
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.
dtt gives the density,
ptt gives the distribution
qtt gives the quantile function, and
generates random deviates.