# tnorm

##### The Truncated Normal Distribution

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

- Keywords
- 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)

rtnorm(n, mean = 0, sd = 1, left = -Inf, right = Inf)

qtnorm(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].

##### 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

*Documentation reproduced from package crch, version 1.0-4, License: GPL-2 | GPL-3*