cnorm: The Censored Normal Distribution

In crch: Censored Regression with Conditional Heteroscedasticity

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.

See Also

dnorm

crch documentation built on Sept. 30, 2024, 9:22 a.m.