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Add yule simon distribution lpmf #3219

@lingium

Description

@lingium

This issue is a feature proposal.

Yule-Simon distribution is a one-parameter discrete distribution, often used to model power-law distributed count data. It is a "better to use in practice" version of Zipf/Zeta distribution, which we wanted many years ago (#28). Yule-simon is very stable and super fast compared with evaluating Riemann zeta function.

PMF

$$ f(n; \alpha) = \alpha \text{Beta}(n,\alpha+1), \quad n=1,2,... \quad \alpha>0 $$

Wikipedia

SciPy

Expected Output

real yule_simon_lpmf(ints n, reals alpha)

Checklist

This will require ayule_simon_lpmf with analytical derivatives.

  • _lpmf
  • test of _lpmf

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