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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.

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 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 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.

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.

Distributions of index terms have been used in modelling information retrieval systems and databases. Most previous models used some form of the Zipf distribution. This work uses a probability model of the occurrence of index terms to derive discrete distributions which are mixtures of Poisson and negative binomial distributions. These distributions, the generalised inverse Gaussian‐Poisson and the Generalised Waring give better fits than the simpler Zipf distribution, particularly in the tails of the distribution where the high frequency terms are found. They have the advantage of being more explanatory and can incorporate a time parameter if necessary.

Ajiferuke showed that observed author distributions can best be described by a shifted inverse Gaussian‐Poisson distribution. Yet, in the framework of a model to explain observed fractional distributions of authors it is important to know whether a simple one‐parameter distribution such as a geometric or a truncated Poisson can adequately describe observed author distributions, at least in those fields where the single author is still dominant. In this article it is shown that for the field of information science this is indeed the case.

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.