The Truncated Normal Distribution
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) 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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
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]. |
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/σ φ((x - μ)/σ) / (Φ((right - μ)/σ) - Φ((left - μ)/σ))
for left ≤ x ≤ right, and 0 otherwise.
Φ and φ are the cumulative distribution function and probability density function of the standard normal distribution respectively, μ is the mean of the distribution, and σ the standard deviation.
dtnorm gives the density, ptnorm gives the distribution
function, qtnorm gives the quantile function, and rtnorm
generates random deviates.
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