VGAM (version 0.8-4.1)

Bisa: 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. If length(n) > 1 then the length is taken to be the number required.

shape, scale

the (positive) shape and scale parameters.

log

Logical. If TRUE then the logarithm of the density is returned.

Value

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

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.

See Also

bisa.

Examples

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")