VGAM (version 0.7-5)

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. 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.

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")