Power Laws in the Number of Copies Per Title in Libraries

Background. Power law distributions have been found in many contexts, both natural and social. This study examines one way of applying the power law distribution to characterize the breadth and accessibility of library collections. Objectives. The collections of three libraries were analyzed for evidence of power law distributions with regard to the number of copies per title. Methods. Data gathered at the three libraries were analyzed to obtain the coefficient of determination (R2) between the actual distribution of the number of copies for each library, and the number of copies predicted by a power law model. The slope of the best line fit represents the "power' of the distribution, which determines the shape of the particular power law distribution Residís. The results indicate that the number of copies per title in all three collections do in fact fit the power law distribution. But not merely that: although each library collection strongly resembles a power law distribution, the slope, or "power." of the distribution differs in each case, in a direction that indicates that the underlying theory is sound. The evidence is seen by comparing the results of two of the libraries studied here. As a small academic library with a policy directed at expanding its number of titles at the expense of number of copies, Kenyon College has the "flattest" slope or power; while Oak Park Public Library, a large public collection that must balance breadth with accessibility, has a much "steeper" slope to its distribution of titles to copies. Contributions. The results and methods presented here not only allow librarians to understand their collections in a new fashion, but may also have implications for anyone seeking to manage collections into the future: for example, baskets of securities in financial markets, and investments in weapon systems by militaries. Additionally, the results provide support for the "preferential attachment" explanation of the power law distribution development, an important theoretical issue with possible relevance to both the natural and social sciences, particularly economics.