R - random approximate normal distribution of integers with predefined total

Question

I'm trying to create a dataset of randomly generate values that have some specific properties:

• All positive integers greater than 0
• In two columns (x, y) that have equal sums (sum(x) == sum(y))
• Have approximately a normal distribution

I've succeeded in something that generates data close to what I want, but it is very slow. I suspect it's slow because of the while loops.

simSession <- function(sessionid = 1) {
    s <- data.frame(sessionid = sessionid, userid = seq(1:12))
    total <- sample(48:72, 1)

    mu = total / 4
    sigma = 3

    s$x <- as.integer(rnorm(mean=mu, sd=sigma, n=nrow(s)))
    while(sum(s$x) > total) {
        # i <- sample(nrow(s), 1)
        i <- sample(rep(s$userid, s$x), 1)
        if(s[i, ]$x > 1) {
            s[i, ]$x <- s[i, ]$x - 1
        } else {
            s[i, ]$x = 1
        }
    }

    s$y <- as.integer(rnorm(mean=mu, sd=sigma, n=nrow(s)))
    while(sum(s$y) > sum(s$x)) {
        # i <- sample(nrow(s), 1)
        i <- sample(rep(s$userid, s$y), 1)
        if(s[i, ]$y > 1) {
            s[i, ]$y <- s[i, ]$y - 1
        } else {
            s[i, ]$y = 1
        }
    }

    s$xyr <- s$x / s$y

    return(s)
}

Is there something obvious I'm missing that would make this problem easier or an alternative function that would be faster?

Also, bonus points for being able to specify a parameter that skews the mode left or right.

Answer 1

If you don't mind that expected value and variance are equal, you could use the Poisson distribution:

randgen <- function(n,mu) {
  x <- rpois(n,mu)
  y <- rpois(n,mu)

  d <- sum(y)-sum(x)

  if (d<0) {
    ind <- sample(seq_along(y),-d)
    y[ind] <- y[ind]+1
  } else {
    ind <- sample(seq_along(x),d)
    x[ind] <- x[ind]+1
  }

 cbind(x=as.integer(x),y=as.integer(y))
}

set.seed(42)
rand <- randgen(1000,15)

layout(c(1,2))    
qqnorm(rand[,1]); qqline(rand[,1])
qqnorm(rand[,2]); qqline(rand[,2])

is.integer(rand)
#[1] TRUE

sum(rand<0)
#[1] 0

colSums(rand)
#x     y 
#15084 15084

mean(rand[,1])
#[1] 15.084
mean(rand[,2])
#[1] 15.084

sd(rand[,1])
#[1] 4.086275
sd(rand[,2])
#[1] 3.741249