13.7 Discrete range distribution
13.7.1 Probability mass functions
If \(l, u \in \mathbb{Z}\) are lower and upper bounds (\(l \le u\)), then for any integer \(y \in \{l,\ldots,u\}\), \[ \text{DiscreteRange}(y ~|~ l, u) = \frac{1}{u - l + 1}. \]
13.7.2 Sampling statement
y ~ discrete_range(l, u)
Increment the target log probability density with discrete_range_lupmf(y | l, u)
dropping constant additive terms.
13.7.3 Stan functions
All of the discrete range distributions are vectorized so that the
outcome y and the bounds l, u can be a single integer (type int)
or an array of integers (type int[]).
real discrete_range_lpmf(ints y | ints l, ints u)
The log probability mass function with outcome(s) y in \(l:u\).
real discrete_range_lupmf(ints y | ints l, ints u)
The log probability mass function with outcome(s) y in \(l:u\)
dropping constant additive terms.
real discrete_range_cdf(ints y, ints l, ints u)
The discrete range cumulative distribution function
for the given y, lower and upper bounds.
real discrete_range_lcdf(ints y | ints l, ints u)
The log of the discrete range cumulative distribution function
for the given y, lower and upper bounds.
real discrete_range_lccdf(ints y | ints l, ints u)
The log of the discrete range complementary cumulative distribution function
for the given y, lower and upper bounds.
int discrete_range_rng(ints l, ints u)
Generate a discrete variate between the given lower and upper bounds;
may only be used in transformed data and generated quantities blocks.