How to generate a matrix of Beta or Binomial distribution

Hi folks,

I have a question about how to efficiently produce random numbers from Beta
and Binomial distributions.

For Beta distribution, suppose we have two shape vectors shape1 and shape2.
I hope to generate a 10000 x 2 matrix X whose i th rwo is a sample from
reta(2,shape1[i]mshape2[i]). Of course this can be done via loops:

for(i in 1:10000)
{
X[i,]=rbeta(2,shape1[i],shape2[i])
}

However, the above code is time consuming. It would be better to directly
generate X without any loops. I tried the following code

X<- rbeta(2,shape1,shape2)

No, not quite: this only makes 2 random variates, while before you
made 2*10,000 = 20k. You can make them all in one fell swoop like
this:

X <- rbeta(20000, shape1, shape2)

Now you might ask, "shape1" and "shape2" are only 10k long: how does
this work? R will recycle shape1 and shape2 as needed, so you get a
call as if you actually used

rbeta(20000, c(shape1, shape1), c(shape2, shape2))

or more generally

rbeta(20000, rep(shape1, length.out = 20000), rep(shape2, length.out = 20000))

If I understand your code correctly, you want each row to use the same
shape1/shape2 parameters, so we will need to reshape the result of
rbeta() into a matrix: it turns out that this is actually pretty easy
to do for your case:

matrix(rbeta(20000, shape1, shape2), ncol = 2)

R will get the correct number of rows by default (it does the 20000
elements / 2 columns = 10000 rows division internally) and because R
uses column-major ordering, you get the parameter arrangement by happy
coincidence. (Basically, R fills up the first column first, then the
second; this aligns nicely with the recycling behavior in this
problem, so we get back to shape1[1] as soon as we start filling the
second column)

This is a little bit of happy hackery, and you might instead prefer
something more explicit like this:

matrix(rbeta(20000, rep(shape1, each = 2), rep(shape2, each = 2)),
ncol = 2, byrow = TRUE)

which will repeat shape1 and shape2 elementwise two times (so c(1,2,3)
becomes c(1,1,2,2,3,3)) and then fills rowwise. It's a little clearer,
at the expense of verbosity.

but it looks not right. So I was wondering if there is an R code doing this.

For Binomial distribution, I have a similar question.  I hope to generate a
10000 x n matrix Y whose i th row is a sample from rbinom(n,2,p[i]), where p
is a vector of binomial probabilities. We can also do it by loops

for(i in 1:10000)
{
Y[i,]=rbinom(n,2,p[i])
}

This should follow pretty easily from the above.

Hope this helps,
Michael

But it would be nice to do it without using any loops. Is this possible in
R?

Many thanks for great help and suggestions!
Jeff









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