On Thursday, 10 November 2022 at 23:15:24 UTC, H. S. Teoh wrote:
According to the Wikipedia page on multinomial distribution (linked by
Timon), it states that the variance of X_i for n rolls of a k-sided dice
(with probability p_i), where i is a specific outcome, is:
Var(X_i) = np_i(1 - p_i)
Don't really understand where this formula came from (as I said, that page is way above my head), but we can make use of it.
This is where things take a wrong turn. In reality you need more than just a matching mean and variance to correctly simulate some arbitrary probability distribution: https://en.wikipedia.org/wiki/Moment_(mathematics)
Every n-th moment needs to be correct too. Some of these moments have special names (n=1 mean, n=2 variance, n=3 skewness, n=4 kurtosis, ...). If you only take care of the mean and variance for simulating a random distribution, then it's somewhat similar to approximating "sin(x) = x - (x^3 / 3!)" via taking only the first few terms of the Taylor series.
I wonder what's the reason for not using the mir-random library like suggested in the early comments? Do you want to avoid having an extra dependency?
dependency "mir-random" version="~>2.2.19"
import std, mir.random.engine, mir.random.ndvariable;
uint[k] diceDistrib(uint k)(uint N)
in(k > 0)
in(N > 0)
out(r; r.sum == N)
p = 1.0 / k;
auto rv = multinomialVar(N, p);