I just had a quick question that I hope someone can answer. Does anyone know what the distribution of the sum of discrete uniform random variables is? Is it a normal distribution?
Thanks!
I just had a quick question that I hope someone can answer. Does anyone know what the distribution of the sum of discrete uniform random variables is? Is it a normal distribution?
Thanks!
The distribution is asymptotically normal. Otherwise, the exact distribution is that of a normalized extended binomial coefficient, see "Polynomial Coefficients and Distribution of the Sum of Discrete Uniform Variables" by Camila C. S. Caiado and Pushpa N. Rathie at http://community.dur.ac.uk/c.c.d.s.caiado/multinomial.pdf.
So, the idea is to iteratively calculate PMF, using sum of $n-1$ variables to derive PMF of the sum of $n$ variables.
$$P_{a, b, n}(x) = \sum_{i \in a..b} P_{a, b, 1}(i) * P_{a, b, n-1}(x-i)$$
where $P_{a,b,n}$ is the PMF of the sum of $n$ discrete uniform variables.
Notional Python code to calculate the coefficients can be found here.