R: Half-Normal Distribution

dist.HalfNormal {LaplacesDemon} | R Documentation

## 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.

### See Also

`dnorm`, `dnormp`, and `dnormv`.

### 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"))

[Package LaplacesDemon version 16.1.1 Index]