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 0.7-7 Index]