Density, distribution function, quantile function, and random generation for the left and/or right truncated normal distribution.
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)
dtnorm gives the density, ptnorm gives the distribution
function, qtnorm gives the quantile function, and rtnorm
generates random deviates.
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length is
taken to be the number required.
vector of means.
vector of standard deviations.
left censoring point.
right censoring point.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
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.