### Name: lines.saddle.distn
### Title: Add a Saddlepoint Approximation to a Plot
### Aliases: lines.saddle.distn
### Keywords: aplot smooth nonparametric

### ** 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)