Chinese family name distributions in multiple scales

The distribution of Chinese family names is investigated based on data of the fifth national census of China in 2000, including 7329 Chinese family names and 1.28 billion people. The cumulative distribution function (CDF) of family name in multiple scales is presented and the correlation between distribution and scale is discussed. The fitting results show that CDFs at the scales of country, province, city and county all follow stretched exponential truncated power law, while the fitting parameters vary greatly. A characteristic index is proposed to measure the extent the distribution is stretched-exponential-like. The index increases as the scale goes down, indicating that the distribution at lower scale is more stretched-exponential-like, and the distribution at higher scale is more power-law-like. Such correlation between distribution and scale is verified by investigating how the distribution changes as the scale is expanded county by county. Furthermore, the correlation is qualitatively explained by artificially constructing multiple scales with a partition process.