# ct: The Censored Student-t Distribution In crch: Censored Regression with Conditional Heteroscedasticity

 ct R Documentation

## 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)

qct(p, 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)


### 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 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 \tau((x - \mu)/\sigma)/\sigma if left < x < 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.

### Value

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

dt