VGAM (version 0.9-2)

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

Same as in runif.

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, ylim = c(0,1.3), lty = 3,
     main = "X ~ Birnbaum-Saunders(shape, scale = 1)")
lines(x, dbisa(x, shape = 2), col = "orange", 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","orange"), 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, orange 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 = "orange")
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")