(1) Mandelbrot has proposed a generalization of Zipf’s Law. (2) Randomly generated strings follow Zipf’s Law, so some people argue that in some cases it is a statistical artifact.
It seems that power law is really the same as Pareto distribution . This paper gives some closed formulas for distributions of sums of Pareto, which are themselves not Pareto
If two power laws have different parameters, as you go to infinity, odds of encountering the one with higher a becomes vs. one with lower a goes to 0, so I also expect that for large values, heavier tail distribution will dominate
(1) Mandelbrot has proposed a generalization of Zipf’s Law. (2) Randomly generated strings follow Zipf’s Law, so some people argue that in some cases it is a statistical artifact.
http://en.wikipedia.org/wiki/Zipf%27s_law
It seems that power law is really the same as Pareto distribution . This paper gives some closed formulas for distributions of sums of Pareto, which are themselves not Pareto
If two power laws have different parameters, as you go to infinity, odds of encountering the one with higher a becomes vs. one with lower a goes to 0, so I also expect that for large values, heavier tail distribution will dominate
BTW, I also wondered about distribution of bigrams when unigrams are power-law distributed, David Cantrell in sci.math gave an approximate formula for the cdf involving Lambert’s W function
http://groups.google.com/group/sci.math/browse_thread/thread/8de7cee65f65ff70/810470b85f36523b?lnk=st&q=group%3Asci.math#810470b85f36523b
Yaroslav,
Thanks, very useful!
– Panos