Change distribution functions for class structures

[zerothi]

Describe the feature

Distribution functions may be required in 3 different forms:

• delta variants (normal distribution, Cauchy distribution)
• theta variants (Fermi-Dirac distribution)
• integrated $ \int_{-\infty}^x y \delta(y) dy $ which is equivalent to the negative entropy

Since all may be used in either way it would be nice to offload the different distributions to incorporate this.

[zerothi]

@sofiasanz @tfrederiksen this may affect your code since I think the API will change a bit.

I think this is necessary to utilize all different distributions at an equal footing.

[zerothi]

Ideas should probably be extended by scipy stats module. From there

• pdf = delta
• survival function = theta
• entropy, not to be confused with the differential entropy in scipy stats
• interval = support where the differential is nonzero (min/max), this is nice to easily get +- an interesting region. Should be for both delta and theta.