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 0.7-9 Index]