# cnorm: The Censored Normal Distribution In crch: Censored Regression with Conditional Heteroscedasticity

 cnorm R Documentation

## 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)

qcnorm(p, mean = 0, sd = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)

rcnorm(n, mean = 0, sd = 1, 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. 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 \phi((x - \mu)/\sigma)/\sigma if left < x < 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.

dnorm