The Truncated Student-t Distribution

Description

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

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)

qtt(p, 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)

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/((x - )/) / (T((right - )/) - T((left - )/))

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.

See Also

dt