# lines.saddle.distn

##### Add a Saddlepoint Approximation to a Plot

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

- Keywords
- smooth, nonparametric, aplot

##### Usage

```
# S3 method for 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

##### Examples

```
# NOT RUN {
# 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)
# }
```

*Documentation reproduced from package boot, version 1.3-25, License: Unlimited*