Power-law distribution of family names in Japanese societies

We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total number of different family names in a society scales as a power law of the population, (ii) the total number of family names of the same size decreases as the size increases with a power law and (iii) the relation between size and rank of a family name also shows a power law. These scaling properties are found to be consistent for five different regional communities in Japan.