tnorm {crch} | R Documentation |
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.