ABSTRACT
The Beta distribution is a two-parameter distribution which has a finite support set [0, 1]. Because it allows for a wide variety of shapes, it is the primary distribution used to model data with a defined maximum and minimum value. When η > 1 and λ > 1, the distribution is unimodal; when η < 1 and λ < 1, the distribution is U-shaped; when η < 1 and λ ≥ 1 or λ < 1 and η ≥ 1, the distribution is J-shaped or reverse J-shaped; when η = λ, the distribution is symmetric. When η = λ = 1, the distribution reduces to the uniform distribution. As can be seen from the graph, the differential entropy for the Beta distribution is always less than or equal to 0, reaching its maximum value of 0 when it reduces to the uniform distribution on [0, 1]. This is to be expected since the entropy is maximized when all events are equally probable.
