The Distribution of Duplicate Books in University Libraries and its Relationship to Zipf's Law

To investigate the statistical characteristics of the distribution of duplicate books among Japanese university libraries and its relationship to Zipf's law, the union catalog database of Japanese and European language books, maintained at the National Center for Science Information System, was analysed. The investigation included four steps, ① sampling of books from database and tabulation of data, ② specification of models based on Zipf's law, ③ estimation of model parameters, ④ statistical goodness-of-fit test. Statistical analysis applied to both of the size-frequency distribution and the rank-size distribution，revealed that Zipf's law is quite applicable to the distribution of both of the books in Japanese and European languages. The models adopted are not the well-known general forms of Zipf's law, that is, size-frequency model g(x)=ax-b and rank-size model f(r)=αr-β or f(r)=α(r十γ)-β (Mandelbrot's law), but the more generally extended forms, that is, size-frequency model, g(x)=a(x+c)-b and rank-size model f(r)=α(r+γ)-β+δ.