bisaUC: The Birnbaum-Saunders Distribution

In VGAM: Vector Generalized Linear and Additive Models

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.
p	vector of probabilities.
n	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.

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 and Kai Huang

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, 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",
     main = "Blue is density, orange is the CDF", las = 1,
     sub = "Red lines are the 10,20,...,90 percentiles",
     ylab = "", 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 = "red", lty = 3, type = "h")
pbisa(Q, shape = shape) - probs  # Should be all zero
abline(h = probs, col = "red", lty = 3)
lines(Q, pbisa(Q, shape = shape), col = "red", lty = 3, type = "h")

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.