The Folded-Normal Distribution

Density, distribution function, quantile function and random generation for the (generalized) folded-normal distribution.

Usage

dfoldnorm(x, mean = 0, sd = 1, a1 = 1, a2 = 1, log = FALSE)
pfoldnorm(q, mean = 0, sd = 1, a1 = 1, a2 = 1,
          lower.tail = TRUE, log.p = FALSE)
qfoldnorm(p, mean = 0, sd = 1, a1 = 1, a2 = 1,
          lower.tail = TRUE, log.p = FALSE, ...)
rfoldnorm(n, mean = 0, sd = 1, a1 = 1, a2 = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as rnorm.

mean, sd

see rnorm.

a1, a2

see foldnormal.

log

Logical. If TRUE then the log density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

...

Arguments that can be passed into uniroot.

Value

dfoldnorm gives the density, pfoldnorm gives the distribution function, qfoldnorm gives the quantile function, and rfoldnorm generates random deviates.

Author

T. W. Yee and Kai Huang. Suggestions from Mauricio Romero led to improvements in qfoldnorm().

Details

See foldnormal, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

Examples

if (FALSE) { # \dontrun{
m <- 1.5; SD <- exp(0)
x <- seq(-1, 4, len = 501)
plot(x, dfoldnorm(x, m = m, sd = SD), type = "l", ylim = 0:1,
     ylab = paste("foldnorm(m = ", m, ", sd = ",
                  round(SD, digits = 3), ")"), las = 1,
     main = "Blue is density, orange is CDF", col = "blue",
     sub = "Purple lines are the 10,20,...,90 percentiles")
abline(h = 0, col = "gray50")
lines(x, pfoldnorm(x, m = m, sd = SD), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qfoldnorm(probs, m = m, sd = SD)
lines(Q, dfoldnorm(Q, m, SD), col = "purple", lty = 3, type = "h")
lines(Q, pfoldnorm(Q, m, SD), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pfoldnorm(Q, m = m, sd = SD) - probs))  # Should be 0
} # }