JuliaDynamics / ComplexityMeasures.jl

Estimators for probabilities, entropies, and other complexity measures derived from data in the context of nonlinear dynamics and complex systems
MIT License
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Implement `entropy_maximum` for `Kaniadakis` entropy #183

Open kahaaga opened 1 year ago

kahaaga commented 1 year ago

Describe the feature you'd like to have

In #182 the Kaniadakis entropy was introduced. However, the book which gives the formula doesn't state for which discrete probability distribution it is maximised, so entropy_maximum just throws an error for now.

It would be nice to be able to compute the maximum discrete Kaniadakis entropy too.

Cite scientific papers related to the feature/algorithm

The formula for the maximum Kaniadakis entropy as a function of the number of samples is probably given in the literature somewhere, but I haven't seen it yet. A good starting point is to follow the references in Tsallis (2009) book, which gives the definition of Kaniadakis entropy.

Tsallis, C. (2009). Introduction to nonextensive statistical mechanics: approaching a complex world. Springer, 1(1), 2-1.