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Density, distribution function, quantile function, and random generation
for the truncated normal distribution with parameters mean
,
sd
, min
, and max
.
dnormTrunc(x, mean = 0, sd = 1, min = -Inf, max = Inf)
pnormTrunc(q, mean = 0, sd = 1, min = -Inf, max = Inf)
qnormTrunc(p, mean = 0, sd = 1, min = -Inf, max = Inf)
rnormTrunc(n, mean = 0, sd = 1, min = -Inf, max = Inf)
vector of quantiles.
vector of quantiles.
vector of probabilities between 0 and 1.
sample size. If length(n)
is larger than 1, then length(n)
random values are returned.
vector of means of the distribution of the non-truncated random variable.
The default is mean=0
.
vector of (positive) standard deviations of the non-truncated random variable.
The default is sd=1
.
vector of minimum values for truncation on the left. The default value is
min=-Inf
.
vector of maximum values for truncation on the right. The default value is
max=Inf
.
dnormTrunc
gives the density, pnormTrunc
gives the distribution function,
qnormTrunc
gives the quantile function, and rnormTrunc
generates random
deviates.
See the help file for the normal distribution for information about the density and cdf of a normal distribution.
Probability Density and Cumulative Distribution Function
Let min=
max=
|
0 | for |
|
for |
|
1 | for |
Quantiles
The
|
|
for |
|
for |
|
|
for |
Random Numbers
Random numbers are generated using the inverse transformation method:
Mean and Variance
The expected value of a truncated normal random variable with parameters
mean=
sd=
min=
max=
The variance of this random variable is given by:
Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.
Johnson, N. L., S. Kotz, and N. Balakrishnan. (1994). Continuous Univariate Distributions, Volume 1. Second Edition. John Wiley and Sons, New York.
Schneider, H. (1986). Truncated and Censored Samples from Normal Populations. Marcel Dekker, New York, Chapter 2.
# NOT RUN {
# Density of a truncated normal distribution with parameters
# mean=10, sd=2, min=8, max=13, evaluated at 10 and 11.5:
dnormTrunc(c(10, 11.5), 10, 2, 8, 13)
#[1] 0.2575358 0.1943982
#----------
# The cdf of a truncated normal distribution with parameters
# mean=10, sd=2, min=8, max=13, evaluated at 10 and 11.5:
pnormTrunc(c(10, 11.5), 10, 2, 8, 13)
#[1] 0.4407078 0.7936573
#----------
# The median of a truncated normal distribution with parameters
# mean=10, sd=2, min=8, max=13:
qnormTrunc(.5, 10, 2, 8, 13)
#[1] 10.23074
#----------
# A random sample of 3 observations from a truncated normal distribution
# with parameters mean=10, sd=2, min=8, max=13.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(20)
rnormTrunc(3, 10, 2, 8, 13)
#[1] 11.975223 11.373711 9.361258
# }
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