LaplacesDemon: dist.HalfNorm – R documentation

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dist.HalfNorm

Half-Normal Distribution

Description

These functions provide the density, distribution function, quantile function, and random generation for the half-normal distribution.

Usage

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))

Arguments

`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 sigma, which must be positive.
`log,log.p`	Logical. If `log=TRUE`, then the logarithm of the density or result is returned.
`lower.tail`	Logical. If `lower.tail=TRUE` (default), probabilities are Pr[X <= x], otherwise, Pr[X > x].

Details

Application: Continuous Univariate
Density: p(theta) = 2*sigma/pi e^-(theta^2*sigma^2/pi), theta >= 0
Inventor: Derived from the normal or Gaussian
Notation 1: theta ~ HALF-N(sigma)
Notation 2: p(theta) = HN(theta | sigma)
Parameter 1: scale parameter sigma > 0
Mean: E(theta) = 1 / sigma
Variance: var(theta) = (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.

Value

dhalfnorm gives the density, phalfnorm gives the distribution function, qhalfnorm gives the quantile function, and rhalfnorm generates random deviates.

Examples

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"))

LaplacesDemon

Complete Environment for Bayesian Inference

v16.1.4

MIT + file LICENSE

Authors

Byron Hall [aut], Martina Hall [aut], Statisticat, LLC [aut], Eric Brown [ctb], Richard Hermanson [ctb], Emmanuel Charpentier [ctb], Daniel Heck [ctb], Stephane Laurent [ctb], Quentin F. Gronau [ctb], Henrik Singmann [cre]

Initial release