Betanorm {VGAM} | R Documentation

## The Beta-Normal Distribution

### Description

Density, distribution function, quantile function and random generation for the univariate beta-normal distribution.

### Usage

    dbetanorm(x, shape1, shape2, mean=0, sd=1, log=FALSE)
    pbetanorm(q, shape1, shape2, mean=0, sd=1, lower.tail=TRUE, log.p=FALSE)
    qbetanorm(p, shape1, shape2, mean=0, sd=1)
    rbetanorm(n, shape1, shape2, mean=0, sd=1)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a positive integer of length 1.
`shape1, shape2` | the two (positive) shape parameters of the standard beta distribution. They are called `a` and `b` in `beta`.
`mean, sd` | the mean and standard deviation of the univariate normal distribution.
`log, log.p` | Logical. If `TRUE` then all probabilities `p` are given as `log(p)`.
`lower.tail` | Logical. If `TRUE` then the upper tail is returned, i.e., one minus the usual answer.

### Details

The function `betanormal1`, the VGAM family function for estimating the parameters, has not yet been written.

### Value

`dbetanorm` gives the density, `pbetanorm` gives the distribution function, `qbetanorm` gives the quantile function, and `rbetanorm` generates random deviates.

### Author(s)

T. W. Yee

### Examples

    ## Not run:
    shape1 = 0.1; shape2 = 4; m = 1
    x = seq(-10, 2, len=501)
    plot(x, dbetanorm(x, shape1, shape2, m=m), type="l", ylim=0:1, las=1,
         ylab=paste("betanorm(",shape1,", ",shape2,", m=",m, ", sd=1)", sep=""),
         main="Blue is density, red is cumulative distribution function",
         sub="Purple lines are the 10,20,...,90 percentiles", col="blue")
    lines(x, pbetanorm(x, shape1, shape2, m=m), col="red")
    abline(h=0)
    probs = seq(0.1, 0.9, by=0.1)
    Q = qbetanorm(probs, shape1, shape2, m=m)
    lines(Q, dbetanorm(Q, shape1, shape2, m=m), col="purple",
          lty=3, type="h")
    lines(Q, pbetanorm(Q, shape1, shape2, m=m), col="purple", lty=3, type="h")
    abline(h=probs, col="purple", lty=3)
    pbetanorm(Q, shape1, shape2, m=m) - probs # Should be all 0
    ## End(Not run)

[Package VGAM version 0.7-9 Index]