Nothing
draw.gamma.alpha.less.than.one=function(nrep,alpha,beta){
if (beta<=0){
stop("Scale parameter must be positive!\n")
}
if ((alpha<=0)|(alpha>=1)){
stop("Shape parameter 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)
t=0.07+0.75*sqrt(1-alpha)
b=1+exp(-t)*alpha/t
v=b*u1
w1=(v<=1)
w2=(v>1)
x1=t*(v^(1/alpha))
w11=(u2<=(2-x1)/(2+x1))
w12=(u2<=exp(-x1))
x[i][w1&w11]=x1[w1&w11]
x[i][w1&!w11&w12]=x1[w1&!w11&w12]
x2=-log(t*(b-v)/alpha)
y=x2/t
w21=(u2*(alpha+y*(1-alpha))<=1)
w22=(u2<=y^(alpha-1))
x[i][w2&w21]=x2[w2&w21]
x[i][w2&!w21&w22]=x2[w2&!w21&w22]
index=1*(w1&w11)+1*(w1&!w11&w12)+1*(w2&w21)+1*(w2&!w21&w22)
}
}
x=beta*x
emp.mean=round(mean(x), 5)
emp.var=round(var(x), 5)
theo.mean=alpha*beta
theo.mean=round(theo.mean, 5)
theo.var=alpha*beta^2
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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