Studies on frequency distributions of recorded use for students using academic library collections

Frequency distributions of recorded use for students using academic libraries were analysed using statistical models not previously employed for the purpose. The suitability of the data for such analysis is discussed. Evidence suggested that frequency distributions of recorded library use reflected real differences in amounts of library use by users. A computer simulation of library use by students was used to investigate the effects of competition among users upon distributions of use. Negative binomial probability distributions were found to reproduce some of the observed patterns of user activity, but were rejected on grounds of fit and applicability. Other two and three-parameter probability distributions were considered. A novel modification of the negative binomial distribution (being a Neyman Type A-gamma distribution instead of a Poisson-gamma distribution) gave good fit to frequency distributions of recorded use from various libraries. The fitted parameters appeared to be related to statistics of use for the observed populations, but the diversity observed in reality among users was clearly simplified in a stochastic model with only three parameters. In the second part of the study, methods of using the model were explored. Given stability in two of the three parameters, the model could be scaled with time to predict future frequency distributions. The extrapolation of numbers of non-users from one set of data is described. The effect upon the uptake of titles from a library collection of distributions of activity among students was also considered. By simplifying the model, relationships between the mean use by a group of users and maximum amounts of use by individuals, and between numbers of uses and numbers of titles used are suggested. A key factor in relating user activity to uptake is the extent to which users diversify in their use of titles.