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/((x - )/) / (((right - )/) - ((left - )/))

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

$\mathrm{\Phi }$ and $\varphi$ 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