I am currently fitting above mentioned functions to my data and I can observe, that both lognormal and Weibull are better fits than powerlaw. In literature, it is often suggested, that it is hard to distinguish these functions, but I can in my data.I do not completely understand the differences between them though. What might be an explanation for the underlying process that generates my data that I can infer from these results.Hope someone can help me.
Difference powerlaw, lognormal and streteched exponential (Weibull) function
statistics