Add a Saddlepoint Approximation to a Plot
Usage
lines.saddle.distn(sad.d, dens=T, h=function(u) u, J=function(u) 1,
npts=50, lty=1, ...)
Arguments
sad.d
|
An object of class "saddle.distn" 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=T 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 .
|
Description
This function adds a line corresponding to a saddlepoint density or
distribution function approximation to the current plot.Details
The function uses smooth.spline
to produce the saddlepoint curve. When
dens=T
the spline is on the log scale and when dens=F
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$t0
exp.tL <- linear.approx(exp.boot,L=exp.L)
hist(exp.tL,nclass=50,prob=T)
exp.t0 <- c(0,sqrt(var(exp.boot$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)