crch (version 1.0-4)

# ct: The Censored Student-t Distribution

## Description

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

## Usage

dct(x, location = 0, scale = 1, df, left = -Inf, right = Inf, log = FALSE)pct(q, location = 0, scale = 1, df, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)rct(n, location = 0, scale = 1, df, left = -Inf, right = Inf)qct(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].

## Value

dct gives the density, pct gives the distribution function, qct gives the quantile function, and rct generates random deviates.

## 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 censored student-t distribution has density $$f(x)$$:

 $$T((left - \mu)/\sigma)$$ if $$x \le left$$ $$1 - T((right - \mu)/\sigma)$$ if $$x \ge right$$

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.

dt