VGAM (version 0.9-0)

Fnorm: The Folded-Normal Distribution

Description

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

Usage

dfnorm(x, mean = 0, sd = 1, a1 = 1, a2 = 1)
pfnorm(q, mean = 0, sd = 1, a1 = 1, a2 = 1)
qfnorm(p, mean = 0, sd = 1, a1 = 1, a2 = 1, ...)
rfnorm(n, mean = 0, sd = 1, a1 = 1, a2 = 1)

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Must be a positive integer of length 1.

mean, sd

see rnorm.

a1, a2

see fnormal1.

...

Arguments that can be passed into uniroot.

Value

• dfnorm gives the density, pfnorm gives the distribution function, qfnorm gives the quantile function, and rfnorm generates random deviates.

Details

See fnormal1, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

See Also

fnormal1, uniroot.

Examples

m <- 1.5; SD<-exp(0)
x <- seq(-1, 4, len = 501)
plot(x, dfnorm(x, m = m, sd = SD), type = "l", ylim = 0:1, las = 1,
     ylab = paste("fnorm(m = ", m, ", sd = ", round(SD, dig = 3), ")"),
     main = "Blue is density, red is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles", col = "blue")
lines(x, pfnorm(x, m = m, sd = SD), col = "red")
abline(h = 0)
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qfnorm(probs, m = m, sd = SD)
lines(Q, dfnorm(Q, m = m, sd = SD), col = "purple", lty = 3, type = "h")
lines(Q, pfnorm(Q, m = m, sd = SD), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pfnorm(Q, m = m, sd = SD) - probs)) # Should be 0