Lorenz curves These are plots of cumulative percentage (normally used in economic and social history to plot accumulated wealth). However, they can be used here to plot accumulated name frequency (x axis) against accumulated area (y axis). A surname that aligned on the diagonal (a-d) would have a perfectly even distribution of name-holders such that 10% of the area sample contains 10% of the surname-holders, 50% of its area contains 50% of the name-holder population. Any curve that tends to corner b would illustrate a name in which a large percentage of the name-holders are concentrated in a small percentage of land. [Diagram missing here] All Lorenz curves should be compared against the diagonal. It is possible using the Gini coefficient [link no longer available] to measure the area between the diagonal and the curve, s a fraction of the area below the diagonal. A high concentration of surname-holders in a small area would yield a high Gini co-efficient. Lorenz curves are useful for comparing the differential growth or decline of any two features over time so these curves could be used to compare: the evenness of spread of one surname against another, particularly for different time-frames, the main form of a surname against its known variants. Comprehensive area values can be obtained from the Census Abstracts, and individual volumes of the Victoria County History, and selected values from this site. Comparing Census surname distributions over time There were 383 changes to the boundaries of registration districts from 1841 to 1911, and almost 20,000 to parishes from 1876 to 1972. “These changes mean it is very difficult to compare one census with its predecessor and make the creation of long run time series of raw data impossible.” (Source: Ian Gregory and Paul Ell Breaking the boundaries: geographical approaches to integrating 200 years of the census, Journal of the Royal Statistical Society A, 168(2), 2005, pp419-437.) This problem might not affect the study of a single name, but would have to be taken into consideration by those who are studying the varying distribution of a class of names. For example, if one wished to study how the age-distribution of Welsh surnames in a London registration district varied between 1841 to 1901. Gregory and Ell consider possible ways to overcome the problem for census geographers.