An examination of stochastic models for the number of book circulations in academic libraries - Concerning to a negative binomial distribution

Recently, some library circulation models have been developed, and it has been tried to make use of them for decision making in libraries. One of the main approaches is to use a negative binomial distribution as a book circulation frequency distribution. In this paper, firstly, we try to examine the validity of a negative binomial distribution as a book circulation frequency distribution in comparison to other mixture distributions - beta binomial, Neiman's type A, and logarithmic series distributions. As a result, the examination indicates the superiority of the negative binomial distribution. Secondly, we examine a nonstationary Poisson process model which Q. E. Burrell has developed. It's result clarifies that Burrell's model doesn't be enough to fit the year-by-year change of real circulation frequency distributions of Hiyoshi Library and Information Center in Keio University. So, we modify this model. Our modified model gives a better fitness to real deta than Burrell's model.