x = runif(50)
psi  = max(x)

par (mfrow=c(2,2))


# simultaing from the real distribution to estimate variance of psi (maximum)
psi.samp = NULL
for (i in 1:1000) psi.samp = c(psi.samp, max(runif(50)))
hist(psi.samp,breaks=(80:100)/100)
var(psi.samp)

# nonparametric bootstrap
psi.star = NULL
for (i in 1:1000) psi.star = c(psi.star, max(sample(x,50,rep=T)))
hist(psi.star,breaks=(80:100)/100)
var(psi.star)

# parametric: bootstrap from uniform(0, max of data)
psi.par = NULL
for (i in 1:1000) psi.par = c(psi.par, max(runif(50)*psi))
hist(psi.par,breaks=(80:100)/100)
var(psi.par)