Fnorm {VGAM}R Documentation

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.

Details

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

Value

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

Note

qfnorm runs very slowly because it calls uniroot for each value of the argument p. The solution is consequently not exact; the ... can be used to obtain a more accurate solution if necessary.

Author(s)

T. W. Yee

See Also

fnormal1, uniroot.

Examples

## Not run: 
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), ")"), col="blue",
     main="Blue is density, red is cumulative distribution function",
     sub="Purple lines are the 10,20,...,90 percentiles")
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
## End(Not run)

[Package VGAM version 0.7-7 Index]