Discrete Uniform Distribution

Topics: Probability

Definition

The Discrete Uniform Distribution is a symmetric discrete probability distribution that describes an experiment with $n$ finite possible outcomes that are all equally probable. Thus, every one of the $n$ outcomes has a probability of $\frac{1}{n}$.
Example: fair die with 6 sides.

Probability Mass Function

The Discrete Uniform distribution is non-parametric because we can define the outcomes as a set, and not necessarily as a discrete interval.
But in case of a discrete interval $[a,b]$, the PMF looks as follows:

Cumulative Density Function

In case of a discrete interval $[a,b]$, the CDF can be written as:
$F(k,a,b) = min \left[ max \left( \frac{\lfloor k \rfloor - a + 1}{b - a +1} \right), 1 \right] \quad \quad \quad \quad \quad for\; any\; k$
or simply
$F(k,a,b) = \frac{\lfloor k \rfloor - a + 1}{b - a +1} \quad \quad \quad \quad \quad for\; k \in [a,b]$

References

1. https://en.wikipedia.org/wiki/Discrete_uniform_distribution