Bounded Continuous Distributions
The bounded continuous probabilities have support on a finite interval of real numbers.
Uniform distribution
Probability density function
If \(\alpha \in \mathbb{R}\) and \(\beta \in (\alpha,\infty)\), then for \(y \in [\alpha,\beta]\), \[\begin{equation*} \text{Uniform}(y|\alpha,\beta) = \frac{1}{\beta - \alpha} . \end{equation*}\]
Sampling statement
y ~ uniform(alpha, beta)
Increment target log probability density with uniform_lupdf(y | alpha, beta).
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_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
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.