Entropics.jl is a Julia package for computing the maximum-entropy distribution bounded on a close interval with given median, mean, and variance values.
The package in still under development.
An article introducing this package and its interesting applications is also in preparation.
The most important function provided in Entropics.jl is maxendist, which computes a maximum-entropy distribution with given conditions. For example, we may find the maximum-entropy distribution on interval [0,1] with median 0.3 and mean 0.35, and then examine its median, mean, variance, skewness, kurtosis, and entropy.
julia> using Entropics
julia> d = maxendist(0, 1; median=0.3, mean=0.35)
Entropics.MED110{Float64}(0.0, 1.0, 0.3, -2.134967865645346, 0.8140360297855087, 0.9598690412098198)
julia> median(d)
0.3
julia> mean(d)
0.35
julia> var(d)
0.06861280728114773
julia> skewness(d)
0.6318688292278568
julia> kurtosis(d)
2.405231674579595
julia> entropy(d)
-0.13971378252179312