tt {crch}R Documentation

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)

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/σ τ((x - μ)/σ) / (T((right - μ)/σ) - T((left - μ)/σ))

for left ≤ x ≤ right, and 0 otherwise.

where T and τ are the cumulative distribution function and probability density function of the student-t distribution with df degrees of freedom respectively, μ is the location of the distribution, and σ 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


[Package crch version 1.0-4 Index]