Uniform Distribution
X ~ Uniform(a, b)
Equal-Likelihood Family • Published July 19, 2026
The flat-density distribution: history from Laplace's principle of indifference through the probability integral transform underlying every other simulation method in this series, order-statistic maximum-likelihood estimation (with no calculus involved), and why Fisher information doesn't apply in the usual sense when support depends on the parameters.
This reference sheet requires a free account.
Sign up free to read the full Uniform Distribution reference sheet.
Sign up freePrefer a saved copy?
About This Reference Sheet
The flat-density distribution: history from Laplace's principle of indifference through the probability integral transform underlying every other simulation method in this series, order-statistic maximum-likelihood estimation (with no calculus involved), and why Fisher information doesn't apply in the usual sense when support depends on the parameters.
Support
x ∈ [a, b]
Parameters
a, b ∈ ℝ, a < b (lower, upper bounds)