dist.HalfNormal | R Documentation |
These functions provide the density, distribution function, quantile function, and random generation for the half-normal distribution.
dhalfnorm(x, scale=sqrt(pi/2), log=FALSE)
phalfnorm(q, scale=sqrt(pi/2), lower.tail=TRUE, log.p=FALSE)
qhalfnorm(p, scale=sqrt(pi/2), lower.tail=TRUE, log.p=FALSE)
rhalfnorm(n, scale=sqrt(pi/2))
x , q |
These are each a vector of quantiles. |
p |
This is a vector of probabilities. |
n |
This is the number of observations, which must be a positive integer that has length 1. |
scale |
This is the scale parameter |
log , log.p |
Logical. If |
lower.tail |
Logical. If |
Application: Continuous Univariate
Density: p(\theta) = \frac{2 \sigma}{\pi}
\exp(-\frac{\theta^2 \sigma^2}{\pi}), \quad \theta \ge 0
Inventor: Derived from the normal or Gaussian
Notation 1: \theta \sim \mathcal{HN}(\sigma)
Notation 2: p(\theta) = \mathcal{HN}(\theta | \sigma)
Parameter 1: scale parameter \sigma > 0
Mean: E(\theta) = \frac{1}{\sigma}
Variance: var(\theta) = \frac{\pi-2}{2 \sigma^2}
Mode: mode(\theta) = 0
The half-normal distribution is recommended as a weakly informative prior distribution for a scale parameter that may be useful as an alternative to the half-Cauchy, half-t, or vague gamma.
dhalfnorm
gives the density,
phalfnorm
gives the distribution function,
qhalfnorm
gives the quantile function, and
rhalfnorm
generates random deviates.
dnorm
,
dnormp
, and
dnormv
.
library(LaplacesDemon)
x <- dhalfnorm(1)
x <- phalfnorm(1)
x <- qhalfnorm(0.5)
x <- rhalfnorm(10)
#Plot Probability Functions
x <- seq(from=0.1, to=20, by=0.1)
plot(x, dhalfnorm(x,0.1), ylim=c(0,1), type="l", main="Probability Function",
ylab="density", col="red")
lines(x, dhalfnorm(x,0.5), type="l", col="green")
lines(x, dhalfnorm(x,1), type="l", col="blue")
legend(2, 0.9, expression(sigma==0.1, sigma==0.5, sigma==1),
lty=c(1,1,1), col=c("red","green","blue"))
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