# tt

0th

Percentile

##### The Truncated Student-t Distribution

Density, distribution function, quantile function, and random generation for the left and/or right truncated student-t distribution with df degrees of freedom.

Keywords
distribution
##### Usage
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)
##### Arguments
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].

##### Details

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.

##### Value

dtt gives the density, ptt gives the distribution function, qtt gives the quantile function, and rtt generates random deviates.

dt