Discrete Uniform distribution¶
Story¶
A set of discrete outcomes that can be indexed with sequential integers, and each outcome has equal probability, like rolling a fair die.
Example¶
A monkey can choose from any of \(n\) bananas with equal probability.
Parameters¶
The distribution is parametrized by the high and low allowed values, respectively \(y_\mathrm{high}\) and \(y_\mathrm{low}\).
Support¶
The Discrete Uniform distribution is supported on the set of integers ranging from \(y_\mathrm{low}\) and \(y_\mathrm{high}\), inclusive.
Probability mass function¶
Moments¶
Mean: \(\displaystyle{\frac{y_\mathrm{low} + y_\mathrm{high}}{2}}\)
Variance: \(\displaystyle{\frac{(y_\mathrm{high}  y_\mathrm{low} + 1)^2  1}{12}}\)
Usage¶
Package 
Syntax 

NumPy 

SciPy 

Stan 

Notes¶
This distribution is not included in Stan. Instead, use a Categorical distribution with equal probailities.
In SciPy, this distribution is known as
scipy.stats.randint
. The high parameter is not inclusive; i.e., the set of allowed values includes the low parameter, but not the high. The same is true forrg.integers()
, unless you use theendpoint=True
keyword argument, in which case the high parameter is inclusive.