20.1 Uniform Distribution
20.1.1 Probability Density Function
If \(\alpha \in \mathbb{R}\) and \(\beta \in (\alpha,\infty)\), then for \(y \in [\alpha,\beta]\), \[ \text{Uniform}(y|\alpha,\beta) = \frac{1}{\beta - \alpha} . \]
20.1.2 Sampling Statement
y ~ uniform(alpha, beta)
Increment target log probability density with uniform_lpdf(y | alpha, beta)
dropping constant additive terms.
20.1.3 Stan Functions
real uniform_lpdf(reals y | reals alpha, reals beta)
The log of the uniform density of y given lower bound alpha and upper
bound beta
real uniform_cdf(reals y, reals alpha, reals beta)
The uniform cumulative distribution function of y given lower bound
alpha and upper bound beta
real uniform_lcdf(reals y | reals alpha, reals beta)
The log of the uniform cumulative distribution function of y given
lower bound alpha and upper bound beta
real uniform_lccdf(reals y | reals alpha, reals beta)
The log of the uniform complementary cumulative distribution function
of y given lower bound alpha and upper bound beta
R uniform_rng(reals alpha, reals beta)
Generate a uniform variate with lower bound alpha and upper bound
beta; may only be used in transformed data and generated quantities blocks. For a
description of argument and return types, see section
vectorized PRNG functions.