Library and Information Science

Library and Information Science ISSN: 2435-8495
三田図書館・情報学会 Mita Society for Library and Information Science
〒108‒8345 東京都港区三田2‒15‒45 慶應義塾大学文学部図書館・情報学専攻内 c/o Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
Library and Information Science 27: 55-68 (1989)

原著論文Original Article

図書の貸出頻度を記述する負の二項分布モデルの演繹的導出とその一般化A deductive derivation and a generalization of a negative binomial distribution model describing the frequency of book circulation

図書館情報大学情報学部University of Library and Information Science ◇ 〒305‒8550 茨城県つくば市春日1番2号 ◇ Kasuga 1‒2, Tsukuba-shi, Ibaraki 305‒8550, Japan

受付日:1989年8月3日Received: August 3, 1989
発行日:1990年3月31日Published: March 31, 1990

Recently, some models describing the frequency distribution of the book circulation are proposed. In a previous paper, authors also propose a new model of book circulation distribution which is based on a negative binomial distribution. This model is able to describe varians of book circulation distribution with time.

This paper has two purposes; 1) as a model of the book circulation, mathematically deducting a negative binomial distribution, 2) discussing the validity of the book circulation model which authors proposed and generalizing this model for the change with time.

Consequently, two components of a compound Poisson distribution, a Poisson distribution and a gamma distribution, are deductively derived by considering the nature of book loans, and a negative binomial distribution are deductively derived perfectly.

And the two parameters of this gamma distribution are assumed as functions of time variation for describing varians of book circulation with time. The validity of this assumption and the function of these parameters are discussed. As this function, two expressions are used; 1) the usual expression of obsolescence; a exponential function, 2) an alternative for the expression of obsolescence which is derived from a extended obsolescence model. As a result, a generalized model of book circulation distribution with a extended expression of obsolescence is constructed.

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