Surname frequency distributions

The simplest use that can be made of surname data in human biology is to record and compare frequency distributions. If the surnames of all the members of a population (or of a random sample of it) are arranged in rank order from the most to the least frequent, a series of statements can be made about such matters as the frequency of the most frequent name (or several of the most frequent names). Statements can also be made about rare names, for instance the number of names that occur only once. If the samples are large, the frequency of each common surname should vary only by sampling error and should not be appreciably affected by sample size. The number and proportion of surnames that occur once and only once, however, are very dependent on the sample size: as one begins sampling, every name will be unique, but, since the number of surnames is finite, as one continues sampling one will approach a condition in which all surnames in the sample have been encountered a second time. The same applies, although less markedly, to surnames that are listed only twice or three times and to other rare surnames. Thus the shape of the curve of the distribution of surname occurrences is dependent on sample size. In comparative studies a very simple solution would be to draw samples of equal size, but I do not think that this has yet been done in surname studies.