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Quentin Burrell points out that the circulation distribution observed in several library collections is approximately geometric and seeks to explain this phenomenon. He selects one of a number of alternative explanations; that the items in the collection have different levels of ‘popularity’ and that the distribution of popularity is negative exponential: and that for a given popularity the number of borrowings in a time period has a poisson distribution. He proves that this combination does produce a geometric circulation distribution. Finally he introduces a zero‐use category of books which is used to explain the higher than expected number of books that are not borrowed at all in the data. However, alternative models also fit the data and his basic explanation does seem dubious in qualitative terms.

Recent work has demonstrated that stochastic models, incorporating a time parameter, have great potential value for library management in predicting future use of library materials, particularly in the presence of ageing of materials. In this paper a simple empirical Bayes method is presented which avoids the analytic complexity of earlier models and which may therefore be more attractive to the library manager. In particular, the ‘prediction profile’ is advocated as a useful additon to the manager's toolbox.

The Burrell and Cane mixed Poisson model for library loans is used to predict future use of items in a collection. The model is also used to investigate possible relegation procedures based on frequency‐of‐circulation data.

It is shown how the Burrell and Cane mixed Poisson model for library loans can be modified to allow for ageing of the items in a collection. In particular, ageing at an exponential rate is discussed and analysed and the model is contrasted with earlier works. The model is illustrated by data collected at the University of Sussex over a four‐year period.

The correlation structure of the Burrell and Cane mixed Poisson model for library loans with ageing is presented and is illustrated by data from the University of Sussex. The approach is compared and contrasted with that originally formulated by Morse and most recently re‐evaluated by Beheshti and Tague. Directions for future investigation are suggested.

It is shown that Trueswell's empirical 80/20 rule arises quite naturally, in general terms at least, from the type of stochastic model for library loans presented by Burrell and Cane. Particular attention is paid to previously suggested uses of the rule in identifying a ‘core collection’ for a library. This emphasizes that the length of the time period considered is of crucial importance.

Recent work has shown that potentially useful predictions of the circulation of library materials can be made which do not require very restrictive assumptions about underlying probability distributions. In the same spirit, we here consider one of the classic problems of bibliometrics, viz. predicting the number of ‘new’ journals carrying ‘relevant’ articles in the future, using both established parametric approaches and the newer, empirical methods.

A probabilistic mechanism is proposed to describe various forms of the Bradford phenomenon reported in bibliometric research. This leads to a stochastic process termed the Waring process, a special case of which seems to conform with the general features of ‘Bradford's Law’. The presence of a time parameter in the model emphasises that we are considering dynamic systems and allows the possibility of predictions being made.

Alternative forms of the desirability distribution for library materials, as defined by the author in an earlier work, are discussed. It is demonstrated that, while several different distributions may adequately describe an observed circulation frequency distribution over a fairly short time period (one year, say), the long‐term implications may be quite different. Some of the statistical aspects are discussed with an eye to ensuring that the most appropriate model is used.

A simple stochastic model for the borrowing of books from a library collection is proposed which explains some observed circulation frequency distributions. Use of the model requires the specification of just two parameters which may be calculated from the circulation statistics for a fixed period of time. These allow one then to make predictions regarding the patterns of likely future usage, and should assist therefore in determining the impact of any proposed relegation policy. The article is illustrated with data from the library of the University of Sussex, the Wishart Library of the University of Cambridge and from the published University of Pittsburgh study. In the latter case our conclusions differ from those of the original investigators.