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.

`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, prob = 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 1.2-24 Index]