Document and User Distributions

This study is based on circulation data collected from six Canadian University Libraries which have automated circulation systems. It reveals that the frequency distributions of transactions over both users and documents are reverse-J shaped, highly positively skewed, and have a long tail. An analysis of the circulation data indicates that (1) the mean of the distribution is neither equal to the variance nor equal to the standard deviation of the distribution, (2) the variance of the distribution is a non-linear function of the mean of the distribution, and  (3) a low percentage of the users in the university libraries make maximum use of circulation service and equal percentage of documents circulated are borrowed frequently.

In an attempt to describe and identify a probability distribution of transactions over  documents and also over users, it has been observed that most size-frequency data of transactions follow a negative binomial distribution. This is the only distribution which fits at least 45% of the empirical distributions at the 0.01 significance level. It was, however, observed that in the majority of the cases, this distribution does not fit the data relating to document distributions, from undergraduate populations. Various probability distributions, namely (1) Poisson, (2) Truncated Poisson (3) Negative binomial, (4) Truncated negative binomial, (5) Geometric, (6) Logarithmic series, (7) Borel-Tanner, (8) Cumulative advantage, (9) Waring, (10) Weibull-discrete and continuous, (11) Zeta, (12) Pearson curves (13) Johnson curves, (14) Pareto, (15) Logistic, (16) Sinh transformation of the variable, and (17) Bradford 'were tried in order to identify the probability density function which can be used to characterise the distribution of transactions. A discrete Weibull distribution using the Napier constant is also defined for the purpose of fitting the empirical data. On the basis of empirical evidence, it is argued that the phenomenon of distribution of transactions is a manifestation of the "success-breeds-success" phenomenon. A few applications of the study are discussed.