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

 tnorm R Documentation

## 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.

dnorm