DOCUMENTATION NOTE. SIMPLE STOCHASTIC MODELS FOR LIBRARY LOANS
| Date | 01 March 1980 |
| Published date | 01 March 1980 |
| Pages | 209-213 |
| DOI | https://doi.org/10.1108/eb026697 |
| Author | D. WORTHINGTON,A. HINDLE |
| Subject Matter | Information & knowledge management,Library & information science |
DOCUMENTATION NOTE
SIMPLE STOCHASTIC MODELS FOR LIBRARY LOANS
A. HINDLE and D. WORTHINGTON
University
of Lancaster
I. GENERAL COMMENTS
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 intro-
duces 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.
Firstly, the negative exponential distribution of popularity is justified as being
the only distribution conforming with a geometric distribution of circulation.
However, the approximate nature of the observed geometric distribution means
that many other distributions are equally justified. The negative exponential
distribution implies that the number of items of differing popularity will form a
smoothly decreasing curve. This is by no means a universally acceptable implica-
tion. Collections are composed of materials of inherently different 'types' such
as specialized research monographs, standard texts, 'popular' accounts and so on.
These thoughts would lead to notions of discrete popularity classes possibly with
quite widely different levels of inherent demand. Also collections might vary
quite markedly with respect to the overall balance between these different classes
and may not be adequately described in terms of the average demand.
Secondly the poisson distribution for borrowing is suspect for titles in high
demand because although demands may arrive at random there will be a signifi-
cant probability of failure because the book is in use. The binomial distribution
may be more suitable in this situation in that a finite number of periods during
the year could be considered during each of which the book could only be bor-
rowed once. However, this particular variation on Burrell's model is unlikely to
produce significantly different answers in terms of decisions on relegations.
The third aspect of the Burrell model is the introduction of the zero-use cate-
gory. Burrell argues that much zero-use arises from the non-availability of
certain titles. However, the number of
these
books is simply chosen in order to
make the model 'fit'. It seems equally plausible to blame the lack of fit on an
incorrect popularity model. This is a crucial issue because Burrell uses the model
for relegation decisions which require accurate predictions of demand for un-
popular books.
Journal
of
Documentation,
Vol. 36, No. 3, September
1980,
pp. 209-213.
209
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