# Generating from a binomial distribution whose quantile is given

by Jimmy Dur   Last Updated April 11, 2018 18:19 PM

I am trying to reproduce a simulation study in a paper.To do it, I need to generate counts for control and treatment groups as described below,

generate \$θ_{i1}\$ from \$Uni(0.1, 0.2)\$ for \$i = 1, . . . ,k_{0}\$ and set \$θ_{i2} =θ_{i1}\$ for \$i=1, . . . ,k_{0}\$. Set \$θ_{i1}= 0.2\$ and \$θ_{i2}= 0.5\$ for \$i =k_{0}+1,...,k\$. Set \$n=40\$, and for each \$j ∈ {1, 2}\$ and \$i\$, generate a count \$C_{ji}\$ from the binomial distribution \$Bin(θ_{ji}, n)\$ whose quantile is \$u_{i}\$.

for a given \$u\$, I am trying to generate counts \$C_{ji}\$ but I am not sure if I am doing it correctly. Based on my understanding, I wrote down the following R code. And it always gives \$C_{1j}=C_{2j}\$ for all \$j=1,...,k_{0}\$. I don't think this is the data generated for the simulations in the paper I am following. I may be misunderstanding something. I would appreciate if one can help me out.

``````k=10;k0=8;n=40
u=c(0.017,0.017,0.2296,0.6251,0.539,0.66,0.03,0.99,0.0091,0.00028)

#obtain p0 and p1
θ1=c(runif(k0,0.2,0.3),rep(0.3,k-k0))
θ2=c(p0[1:k0],rep(0.7,k-k0))

c1<-numeric(k)
for (i in 1:k){
c1[i]=qbinom(u[i],n,θ1[i])
}

c2<-numeric(k)
for (i in 1:k){
c2[i]=qbinom(u[i],n,θ2[i])
}
``````
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