A SECOND NOTE ON AGEING IN A LIBRARY CIRCULATION MODEL: THE CORRELATION STRUCTURE
| Date | 01 February 1986 |
| Published date | 01 February 1986 |
| Pages | 114-128 |
| DOI | https://doi.org/10.1108/eb026789 |
| Author | QUENTIN L. BURRELL |
| Subject Matter | Information & knowledge management,Library & information science |
A SECOND NOTE ON AGEING IN A LIBRARY
CIRCULATION MODEL: THE CORRELATION STRUCTURE
QUENTIN L. BURRELL
Statistical Laboratory
Department
of
Mathematics,
The
University,
Manchester,
M13 9PL
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.
1.
INTRODUCTION
IN A PREVIOUS PAPER Burrell1 demonstrated how the mixed Poisson model
for library loans presented by Burrell and Cane2 (but see also Burrell3,4 for less
technical descriptions) could be modified in
a
simple way to accommodate the em-
pirical phenomenon of ageing of the collection under consideration. Roughly
speaking, the modification assumes that the observed decline in mean borrowing
is a reflection of
an
inherent decline in the 'desirability' (see Burrell3) of the items
in the collection, the rate of this decline being assumed to be the same for all items.
In this paper we focus on the year-by-year use of
items
and investigate the cor-
relation structure arising from the model. We shall in particular compare and con-
trast the implications of this model with those of Beheshti and Tague5 who
recently reconsidered Morse's6 original Markov-Poisson model, and of Bagust's7
approach to the mixed Poisson model.
The paper should be regarded
as a
continuation of Burrell1 and the notation and
usage of terms are
as
described there. The main features of the model, and applica-
tions,
are presented in the following sections while all mathematical details have
been deferred to an Appendix.
2.
THE CORRELATION PHENOMENON
One of the most interesting - and striking - features of library circulation data
arises when we consider the numbers of loans of items in two consecutive time
periods (usually these would be one-year periods). If we find N(m), the mean
number of loans during the second period of
all
items which were loaned m times
during the first period, for m = 0,1,2,..., then the plot of N(m) against m is (at
least approximately) linear. A good example of this empirical phenomenon is
given in Figure 1 which is taken from Burrell and Cane2 and is based on data
generated by the short-loan collection of the University of Sussex Library.
Many other examples exist in the literature, based on both small and large data
sets and relating to subject-defined as well as general collections. Several of the
reported instances refer to the original classic work of Morse6 in which the circula-
Journal
of
Documentation,
Vol. 42, No. 2, June 1986, pp. 114-128.
114
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