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24.1 Uniform distribution

24.1.1 Probability density function

If $\alpha \in \mathbb{R}$ and $\beta \in (\alpha,\infty)$, then for $y \in [\alpha,\beta]$, $$\text{Uniform}(y|\alpha,\beta) = \frac{1}{\beta - \alpha} .$$

24.1.2 Sampling statement

y ~ uniform(alpha, beta)

Increment target log probability density with uniform_lupdf(y | alpha, beta).
Available since 2.0

24.1.3 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
Available since 2.12

real uniform_lupdf(reals y | reals alpha, reals beta)
The log of the uniform density of y given lower bound alpha and upper bound beta dropping constant additive terms
Available since 2.25

real uniform_cdf(reals y, reals alpha, reals beta)
The uniform cumulative distribution function of y given lower bound alpha and upper bound beta
Available since 2.0

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
Available since 2.12

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
Available since 2.12

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.
Available since 2.18