Question

How can I make my own function for rbinom(n, size, prob) in R.

So, basically I want to build my own rbinom function that gives me the same result as rbinom that's built in R software.

Answer 1

The function is below

R code with comments (all statements starting with # are comments)

#define the rbinom function
myRbinom<-function(n,size,prob){
   #draw n*size numbers from uniform random (0,1)
   u<-runif(n*size)
   #arrange this into a matrix of size (n x size): n rows and size columns
   u<-matrix(u,nrow=n,ncol=size)
   #set the values which are less than prob as success
   success<-u<prob
   #count the number of successes for each row
   x<-apply(success,1,sum)
   return(x)
}

## now let us try this out for number of trials = 10 and success probability =0.2.

We know that the theoretical mean for a Binomial distribution (or the expectation) is trials*prob = 10*0.2=2

the theoretical variance is trials*prob*(1-prob) = 10*0.2*0.8=1.6

Let us see if we can get these values

R code

#set the random seed
set.seed(123)
n<-10000
size<-10
p<-0.2
y<-myRbinom(n,size,p)
#Check if this looks good
sprintf('Estimated mean of y is %.4f',mean(y))
sprintf('Estimated variance of y is %.4f',var(y))
sprintf('The theoretical mean of Y (E[Y]) is %.4f',size*p)
sprintf('The theoretical variance of Y is %.4f',size*p*(1-p))

## get this output

the estimated mean and variances are close to the theoretical values. Hence the function looks good.