### Abstract

The purpose of this paper is to propose a new mathematical model for predicting the amount of loan at public libraries, and to investigate the validity of the model by using statistical data on public libraries at Saitama Prefecture in Japan. The model is L=aCPexp (-bC), where L is the number of times books are circulated in a library, C is the number of books held at the library, P is the population within the service area, and a and b are parameters. The model explains well statistical variation of the amount of loan at Saitama Prefecture. It can be said that the result shows a sort of "inverse effect" of size of collection or population, which is represented by exp (-bC) in the model, on the increase in loan. Also, a simple simulation based on the model is tried to assess the effectiveness of new sites for access.

Original language | English |
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Pages (from-to) | 29-35 |

Number of pages | 7 |

Journal | Library and Information Science |

Volume | 40 |

Publication status | Published - 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Library and Information Sciences

### Cite this

**A mathematical model on public library loan incorporating an inverse size effect.** / Kishida, Kazuaki.

Research output: Contribution to journal › Article

*Library and Information Science*, vol. 40, pp. 29-35.

}

TY - JOUR

T1 - A mathematical model on public library loan incorporating an inverse size effect

AU - Kishida, Kazuaki

PY - 1998

Y1 - 1998

N2 - The purpose of this paper is to propose a new mathematical model for predicting the amount of loan at public libraries, and to investigate the validity of the model by using statistical data on public libraries at Saitama Prefecture in Japan. The model is L=aCPexp (-bC), where L is the number of times books are circulated in a library, C is the number of books held at the library, P is the population within the service area, and a and b are parameters. The model explains well statistical variation of the amount of loan at Saitama Prefecture. It can be said that the result shows a sort of "inverse effect" of size of collection or population, which is represented by exp (-bC) in the model, on the increase in loan. Also, a simple simulation based on the model is tried to assess the effectiveness of new sites for access.

AB - The purpose of this paper is to propose a new mathematical model for predicting the amount of loan at public libraries, and to investigate the validity of the model by using statistical data on public libraries at Saitama Prefecture in Japan. The model is L=aCPexp (-bC), where L is the number of times books are circulated in a library, C is the number of books held at the library, P is the population within the service area, and a and b are parameters. The model explains well statistical variation of the amount of loan at Saitama Prefecture. It can be said that the result shows a sort of "inverse effect" of size of collection or population, which is represented by exp (-bC) in the model, on the increase in loan. Also, a simple simulation based on the model is tried to assess the effectiveness of new sites for access.

UR - http://www.scopus.com/inward/record.url?scp=25144433561&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25144433561&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:25144433561

VL - 40

SP - 29

EP - 35

JO - Library and Information Science

JF - Library and Information Science

SN - 0373-4447

ER -