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

`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)

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].

`dcnorm`

gives the density, `pcnorm`

gives the distribution
function, `qcnorm`

gives the quantile function, and `rcnorm`

generates random deviates.

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.