# cnorm

##### The Censored Normal Distribution

Density, distribution function, quantile function, and random generation for the left and/or right censored normal distribution.

- Keywords
- distribution

##### Usage

`dcnorm(x, mean = 0, sd = 1, left = -Inf, right = Inf, log = FALSE)`pcnorm(q, mean = 0, sd = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)

rcnorm(n, mean = 0, sd = 1, left = -Inf, right = Inf)

qcnorm(p, mean = 0, sd = 1, 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.- mean
vector of means.

- sd
vector of standard deviations.

- 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 `mean`

or `sd`

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 normal distribution has density \(f(x)\):

\(\Phi((left - \mu)/\sigma)\) | if \(x \le left\) |

\(1 - \Phi((right - \mu)/\sigma)\) | if \(x \ge right\) |

where \(\Phi\) and \(\phi\) are the cumulative distribution function and probability density function of the standard normal distribution respectively, \(\mu\) is the mean of the distribution, and \(\sigma\) the standard deviation.

##### Value

`dcnorm`

gives the density, `pcnorm`

gives the distribution
function, `qcnorm`

gives the quantile function, and `rcnorm`

generates random deviates.

##### See Also

*Documentation reproduced from package crch, version 1.0-4, License: GPL-2 | GPL-3*