Discrete Uniform Distribution
X ~ DiscreteUniform(a, b)
Equal-Likelihood Family • Published July 20, 2026
The distribution of a fair die or any lottery drawing: history reaching back to Cardano and the Fermat-Pascal correspondence, the famous World War II 'German Tank Problem' application, why it is the maximum-entropy distribution over a fixed set of outcomes, why Fisher information doesn't apply for the same structural reason as the continuous Uniform, order-statistic maximum-likelihood estimation with no clean bias-correction formula, and direct simulation.
This reference sheet requires a free account.
Sign up free to read the full Discrete Uniform Distribution reference sheet.
Sign up freePrefer a saved copy?
About This Reference Sheet
The distribution of a fair die or any lottery drawing: history reaching back to Cardano and the Fermat-Pascal correspondence, the famous World War II 'German Tank Problem' application, why it is the maximum-entropy distribution over a fixed set of outcomes, why Fisher information doesn't apply for the same structural reason as the continuous Uniform, order-statistic maximum-likelihood estimation with no clean bias-correction formula, and direct simulation.
Support
x ∈ {a, a+1, ..., b}
Parameters
a, b ∈ ℤ, a ≤ b