VGAM (version 1.0-3)

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.

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.

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.

References

Lemonte, A. J. and Cribari-Neto, F. and Vasconcellos, K. L. P. (2007) Improved statistical inference for the two-parameter Birnbaum-Saunders distribution. Computational Statistics \& Data Analysis, 51, 4656--4681.

Birnbaum, Z. W. and Saunders, S. C. (1969) A new family of life distributions. Journal of Applied Probability, 6, 319--327.

Birnbaum, Z. W. and Saunders, S. C. (1969) Estimation for a family of life distributions with applications to fatigue. Journal of Applied Probability, 6, 328--347.

Engelhardt, M. and Bain, L. J. and Wright, F. T. (1981) Inferences on the parameters of the Birnbaum-Saunders fatigue life distribution based on maximum likelihood estimation. Technometrics, 23, 251--256.

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, 2nd edition, Volume 2, New York: Wiley.

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", 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")
# }