Continuously go from a lognormal distribution to a power law

Question

Do you know any phenomena that are described by a continuous mappings between a lognormal and a power law distribution?

Of course, one could give a simple linear combination of the two distributions; I am interested to mechanisms that actually arise in nature.

Answer 1

If you impose a minimum boundary a Geometric Brownian Motion you get a power law distribution when solving the respective Fokker Planck equation.

You may look up Gabaix 1999 and Kesten 1973.