tnorm: The Truncated Normal Distribution

In crch: Censored Regression with Conditional Heteroscedasticity

The Truncated Normal Distribution

Description

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

Usage

dtnorm(x, mean = 0, sd = 1, left = -Inf, right = Inf, log = FALSE)

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

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

rtnorm(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 truncated normal distribution has density

f(x) = 1/\sigma \phi((x - \mu)/\sigma) / (\Phi((right - \mu)/\sigma) - \Phi((left - \mu)/\sigma))

for left \le x \le right, and 0 otherwise.

\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

dtnorm gives the density, ptnorm gives the distribution function, qtnorm gives the quantile function, and rtnorm generates random deviates.

See Also

dnorm

crch documentation built on April 4, 2025, 3:29 a.m.