Bisa {VGAM}R Documentation

The Birnbaum-Saunders Distribution

Description

Density, distribution function, and random generation for the Birnbaum-Saunders distribution.

Usage

dbisa(x, shape, scale=1, log=FALSE)
pbisa(q, shape, scale=1)
qbisa(p, shape, scale=1)
rbisa(n, shape, scale=1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. Must be a positive integer of length 1.
shape, scale the (positive) shape and scale parameters.
log Logical. If TRUE then the logarithm of the density is returned.

Details

The Birnbaum-Saunders distribution is a distribution which is used in survival analysis. See bisa, the VGAM family function for estimating the parameters, for more details.

Value

dbisa gives the density, pbisa gives the distribution function, and qbisa gives the quantile function, and rbisa generates random deviates.

Author(s)

T. W. Yee

See Also

bisa.

Examples

## Not run: 
x = seq(0, 6, len=400)
plot(x, dbisa(x, shape=1), type="l", col="blue", ylab="Density", lwd=2,
     main="X ~ Birnbaum-Saunders(shape, scale=1)", ylim=c(0,1.3), lty=3)
lines(x, dbisa(x, shape=2), col="red", lty=2, lwd=2)
lines(x, dbisa(x, shape=0.5), col="green", lty=1, lwd=2)
legend(x=3, y=0.9, legend=paste("shape =",c(0.5,1,2)),
       col=c("green","blue","red"), lty=1:3, lwd=2)

shape = 1
x = seq(0.0, 4, len=401)
plot(x, dbisa(x, shape=shape), type="l", col="blue", las=1, ylab="",
     main="Blue is density, red is cumulative distribution function",
     sub="Purple lines are the 10,20,...,90 percentiles", ylim=0:1)
abline(h=0, col="blue", lty=2)
lines(x, pbisa(x, shape=shape), col="red")
probs = seq(0.1, 0.9, by=0.1)
Q = qbisa(probs, shape=shape)
lines(Q, dbisa(Q, shape=shape), col="purple", lty=3, type="h")
pbisa(Q, shape=shape) - probs    # Should be all zero
abline(h=probs, col="purple", lty=3)
lines(Q, pbisa(Q, shape), col="purple", lty=3, type="h")
## End(Not run)

[Package VGAM version 0.7-7 Index]