Journal Article10.1108/EB026697
Documentation note: simple stochastic models for library loans
David Worthington,Anthony Hindle +1 more
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TL;DR: Quentin Burrell points out that the circulation distribution observed in several library collections is approximately geometric and seeks to explain this phenomenon and 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.
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Abstract: 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.
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Citations
The 80/20 rule: library lore or statistical law?
TL;DR: 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.
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A circulation model for busy public libraries
TL;DR: A stochastic model of library borrowing using the Negative Binomial distribution is developed, which shows an improvement over previous characterizations for academic libraries and accords well with new data obtained at Huddersfield Public Library.
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A third note on aging in a library circulation model: Applications to future use and relegation
TL;DR: The Burrell and Cane mixed Poisson model for library loans is used to predict future use of items in a collection and is also used to investigate possible relegation procedures based on frequency‐of‐circulation data.
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Alternative Models for Library Circulation Data.
TL;DR: It is demonstrated that, while several different distributions may adequately describe an observed circulation frequency distribution over a fairly short time period, the long‐term implications may be quite different.
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References
A simple stochastic model for library loans
TL;DR: A simple stochastic model for the borrowing of books from a library collection is proposed which explains some observed circulation frequency distributions and should assist therefore in determining the impact of any proposed relegation policy.