library(bootstrap)
za <- function(z0,a,alpha)
{
  num <- z0 + qnorm(alpha)
  denom <- 1 - a*(z0 + qnorm(alpha))
  z0 + num/denom
}

alpha <- seq(0.001,0.999,0.001)
plot(za(0,0,alpha) ~ alpha)
plot(za(0,0.1,alpha) ~ alpha)
plot(za(0,0.2,alpha) ~ alpha)
plot(za(0,0.3,alpha) ~ alpha)
plot(za(0,0.4,alpha) ~ alpha)

x <- rnorm(2000)
b <- bcanon(x,theta = mean,nboot = 100)
b$acc

#from the normal theory: sd(var hat) proportional to real sd
func <- function(mu,s) sd(rnorm(100,mu,s))
sds <- replicate(2000,func(0,10))
sd(sds)

norms <- rnorm(100,0,25)
b <- bcanon(norms,100,theta=sd)
b$acc

norms2 <- exp(norms)
b2 <- bcanon(norms2,100,theta=sd)
b2$acc