Bisa {VGAM} | R Documentation

## 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` | number of observations. If `length(n) > 1` then the length is taken to be the number required.
`shape, scale` | the (positive) shape and scale parameters.
`log` | Logical. If `TRUE` then the logarithm of the density is returned.

### 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

### 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,
         main="X ~ Birnbaum-Saunders(shape, scale=1)", ylim=c(0,1.3), lty=3)
    lines(x, dbisa(x, shape=2), col="red", 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","red"), 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, red 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="red")
    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")
    ## End(Not run)

[Package VGAM version 0.7-9 Index]