greybox (version 0.6.4)

dfnorm: Folded Normal Distribution

Description

Density, cumulative distribution, quantile functions and random number generation for the folded normal distribution with the location parameter mu and the scale sigma (which corresponds to standard deviation in normal distribution).

Usage

dfnorm(q, mu = 0, sigma = 1, log = FALSE)
pfnorm(q, mu = 0, sigma = 1)
qfnorm(p, mu = 0, sigma = 1)
rfnorm(n = 1, mu = 0, sigma = 1)

Arguments

q

vector of quantiles.

mu

vector of location parameters (means).

sigma

vector of scale parameters.

log

if TRUE, then probabilities are returned in logarithms.

p

vector of probabilities.

n

number of observations. Should be a single number.

Value

Depending on the function, various things are returned (usually either vector or scalar):

• dfnorm returns the density function value for the provided parameters.

• pfnorm returns the value of the cumulative function for the provided parameters.

• qfnorm returns quantiles of the distribution. Depending on what was provided in p, mu and sigma, this can be either a vector or a matrix, or an array.

• rfnorm returns a vector of random variables generated from the fnorm distribution. Depending on what was provided in mu and sigma, this can be either a vector or a matrix or an array.

Details

The distribution has the following density function:

f(x) = 1/sqrt(2 pi) (exp(-(x-mu)^2 / (2 sigma^2)) + exp(-(x+mu)^2 / (2 sigma^2)))

Both pfnorm and qfnorm are returned for the lower tail of the distribution.

References

• Wikipedia page on folded normal distribution: https://en.wikipedia.org/wiki/Folded_normal_distribution.

Examples

# NOT RUN {
x <- dfnorm(c(-1000:1000)/200, 0, 1)
plot(x, type="l")

x <- pfnorm(c(-1000:1000)/200, 0, 1)
plot(x, type="l")

qfnorm(c(0.025,0.975), 0, c(1,2))

x <- rfnorm(1000, 0, 1)
hist(x)

# }