crch (version 1.0-4)

# cnorm: The Censored Normal Distribution

## Description

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

## Value

dcnorm gives the density, pcnorm gives the distribution function, qcnorm gives the quantile function, and rcnorm generates random deviates.

## 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.

dnorm