R: The Birnbaum-Saunders Distribution

Bisa {VGAM} | R Documentation

## 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", 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")

    ## End(Not run)

[Package VGAM version 1.1-3 Index]