Handbook of Differential Entropy

4

Differential Entropies for Probability

Distributions

4.1 Beta Distribution

The Beta distribution is a two-parameter distribution which has a finite sup-

port 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 distri-

bution. As can be seen from the graph, the differen ...