Density, distribution function, quantile function and random generation for
the truncated Normal distribution with mean equal to mean
and
standard deviation equal to sd
before truncation, and truncated on
the interval [lower, upper]
.
dtnorm(x, mean = 0, sd = 1, lower = -Inf, upper = Inf, log = FALSE)ptnorm(
q,
mean = 0,
sd = 1,
lower = -Inf,
upper = Inf,
lower.tail = TRUE,
log.p = FALSE
)
qtnorm(
p,
mean = 0,
sd = 1,
lower = -Inf,
upper = Inf,
lower.tail = TRUE,
log.p = FALSE
)
rtnorm(n, mean = 0, sd = 1, lower = -Inf, upper = 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 means.
vector of standard deviations.
lower truncation point.
upper truncation point.
logical; if TRUE, return log density or log hazard.
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
logical; if TRUE, probabilities p are given as log(p).
vector of probabilities.
number of observations. If length(n) > 1
, the length is
taken to be the number required.
C. H. Jackson chris.jackson@mrc-bsu.cam.ac.uk
The truncated normal distribution has density
$$ f(x, \mu, \sigma) = \phi(x, \mu, \sigma) / (\Phi(u, \mu, \sigma) - \Phi(l, \mu, \sigma)) $$ for \(l <= x <= u\), and 0 otherwise.
\(\mu\) is the mean of the original Normal distribution before
truncation,
\(\sigma\) is the corresponding standard deviation,
\(u\) is the upper truncation point,
\(l\) is the lower
truncation point,
\(\phi(x)\) is the density of the
corresponding normal distribution, and
\(\Phi(x)\) is the
distribution function of the corresponding normal distribution.
If mean
or sd
are not specified they assume the default values
of 0
and 1
, respectively.
If lower
or upper
are not specified they assume the default
values of -Inf
and Inf
, respectively, corresponding to no
lower or no upper truncation.
Therefore, for example, dtnorm(x)
, with no other arguments, is simply
equivalent to dnorm(x)
.
Only rtnorm
is used in the msm
package, to simulate from
hidden Markov models with truncated normal distributions. This uses the
rejection sampling algorithms described by Robert (1995).
These functions are merely provided for completion, and are not optimized
for numerical stability or speed. To fit a hidden Markov model with a
truncated Normal response distribution, use a hmmTNorm
constructor. See the hmm-dists
help page for further details.
Robert, C. P. Simulation of truncated normal variables. Statistics and Computing (1995) 5, 121--125
x <- seq(50, 90, by=1)
plot(x, dnorm(x, 70, 10), type="l", ylim=c(0,0.06)) ## standard Normal distribution
lines(x, dtnorm(x, 70, 10, 60, 80), type="l") ## truncated Normal distribution
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