library(plyr)

create random discrete variables and plot it

discrete_normal_arr <- round(rnorm(1000, 500, 10), 0)
hist(discrete_normal_arr, prob=TRUE, ylim=c(0,.06), breaks=10)
curve(dnorm(x, mean(discrete_normal_arr), sd(discrete_normal_arr)), add=TRUE, col="darkblue", lwd=2)

define shannon entropy

shannon_entropy <- function(x){
  df = count(x)
  n = length(x)
  df$probs = df$freq / n
  se<- -sum(df$probs * log(df$probs))
  return(se)
}

play it

shannon_entropy(discrete_normal_arr)

## [1] 3.719547