Nothing
draw.beta.alphabeta.less.than.one=function(nrep,alpha,beta){
if ((alpha>=1)|(alpha<=0)|(beta>=1)|(beta<=0)) {
stop ("Both shape parameters must be between 0 and 1!\n")
}
x=numeric(nrep)
for (i in 1:nrep){
index=0
while (index<1){
u1=runif(1)
u2=runif(1)
v1=u1^(1/alpha)
v2=u2^(1/beta)
summ=v1+v2
w=(summ<=1)
x[i]=v1/summ
index=sum(w)
}
}
emp.mean=round(mean(x), 5)
emp.var=round(var(x), 5)
theo.mean=(alpha)/(alpha+beta)
theo.mean=round(theo.mean, 5)
theo.var=(alpha*beta)/((alpha+beta)^2*(alpha+beta+1))
theo.var=round(theo.var, 5)
return(list(y=x, theo.mean=theo.mean, emp.mean=emp.mean, theo.var=theo.var, emp.var=emp.var))
}
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