Sampling from a Binomial(K, p) with unexpected result

Question

In the help files for rbinom, size argument is a number of trials (incl. a zero) but it doesn't say if this can also be a vector.

The correct way of using this function is

table(rbinom(n = 1000, size = 1, prob = 0.2))

  0   1 
809 191

But what is happening here?

table(rbinom(n = 1000, size = 0:1, prob = 0.2))

  0   1 
894 106 

Answer 1

Argument recycling of the size argument is the prime cause.

Because n is 1000, 0:1 is recycled until you get 500 0's and 500 1's (alternating).

All the 0-size ones give 0:

   > rbinom(10,size=0,prob=0.2)  
     [1] 0 0 0 0 0 0 0 0 0 0

Resulting in 500 0's + 500 Bernoulli trials with p=0.2, resulting in about 100 1's out of 1000 elements.

[Your results didn't seem surprising to me, but argument recycling can bite if you're not looking for it, and - while there are reasons why the number of successes in 0 Bernoulli trials should be defined as 0 - it may not seem obvious at first either.]