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.

See Also

dnorm