We examine the effect of finite size of population on the distribution of family names. As the result we observe that the power-law behavior of size-frequency distribution in Reed--Hughes () model collapses to show the convex shape on the logarithmic graph. We can approximately calculate the average distribution of size-frequency distribution of family names obtained by the similar method for Ewens sampling formula.
"Effect of the Finite Size of Population on the Distribution of Family Names." Japan J. Indust. Appl. Math. 24 (1) 119 - 130, February 2007.