crch (version 1.0-4)

# tnorm: 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)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].

## Value

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

## 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.

dnorm