R: Add a Saddlepoint Approximation to a Plot

lines.saddle.distn {boot} | R Documentation

## Add a Saddlepoint Approximation to a Plot

### Description

This function adds a line corresponding to a saddlepoint density or distribution function approximation to the current plot.

### Usage

    ## S3 method for class 'saddle.distn'
    lines(x, dens = TRUE, h = function(u) u, J = function(u) 1,
          npts = 50, lty = 1, ...)

### Arguments

`x` | An object of class `"saddle.distn"` (see `saddle.distn.object` representing a saddlepoint approximation to a distribution.
`dens` | A logical variable indicating whether the saddlepoint density (`TRUE`; the default) or the saddlepoint distribution function (`FALSE`) should be plotted.
`h` | Any transformation of the variable that is required. Its first argument must be the value at which the approximation is being performed and the function must be vectorized.
`J` | When `dens=TRUE` this function specifies the Jacobian for any transformation that may be necessary. The first argument of `J` must the value at which the approximation is being performed and the function must be vectorized. If `h` is supplied `J` must also be supplied and both must have the same argument list.
`npts` | The number of points to be used for the plot. These points will be evenly spaced over the range of points used in finding the saddlepoint approximation.
`lty` | The line type to be used.
`...` | Any additional arguments to `h` and `J`.

### Details

The function uses `smooth.spline` to produce the saddlepoint curve. When `dens=TRUE` the spline is on the log scale and when `dens=FALSE` it is on the probit scale.

### Value

`sad.d` is returned invisibly.

### Side Effects

A line is added to the current plot.

### References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

### See Also

`saddle.distn`

### Examples

    # In this example we show how a plot such as that in Figure 9.9 of
    # Davison and Hinkley (1997) may be produced.  Note the large number of
    # bootstrap replicates required in this example.
    expdata <- rexp(12)
    vfun <- function(d, i) {
         n <- length(d)
         (n-1)/n*var(d[i])
    }
    exp.boot <- boot(expdata,vfun, R = 9999)
    exp.L <- (expdata - mean(expdata))^2 - exp.boot$t0
    exp.tL <- linear.approx(exp.boot, L = exp.L)
    hist(exp.tL, nclass = 50, probability = TRUE)
    exp.t0 <- c(0, sqrt(var(exp.boot$t)))
    exp.sp <- saddle.distn(A = exp.L/12,wdist = "m", t0 = exp.t0)

    # The saddlepoint approximation in this case is to the density of
    # t-t0 and so t0 must be added for the plot.
    lines(exp.sp, h = function(u, t0) u+t0, J = function(u, t0) 1,
          t0 = exp.boot$t0)

[Package boot version 1.3-4 Index]