Bisa: The Birnbaum-Saunders Distribution

Description

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

Usage

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

Arguments

x, q

vector of quantiles.

vector of probabilities.

Same as in runif.

scale, shape

the (positive) scale and shape parameters.

log

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

lower.tail, log.p

Same meaning as in pnorm or qnorm.

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.

Examples

Run this code

# NOT RUN {
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 = shape), col = "purple", lty = 3, type = "h")
# }