1998 Fiscal Year Final Research Report Summary
Random partition of a finite set and related fields
| Project/Area Number |
08680333
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Takachiho University |
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Principal Investigator |
SIBUYA Masaaki Takachiho University, Faculty of Commerce, Professor, 商学部, 教授 (20146723)
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| Project Period (FY) |
1996 – 1998
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| Keywords | clustering process / distance between partitions / frequency of frequencies / number of new records / size index / Stirling-Carlitz polynomial / Stirling number of the first kind / the most random partition |
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| Research Abstract |
Random partition appears in the diversity of population in ecology, vocabulary of a group in linguistics, inelastic collision of particles in dynamics etc. and relates to Ziph's law in social groups. It has been advanced recently in population genetics in relation with random occurrence of new alleles.
In this projects, statistical problems in the application of the model and related problems are studied. A central question is the notion of the most random partition of a finite set. This notion can be applied to the clustering technique in multivariate data analysis. Any method can be justified only if it classifies meaningful data in a systematic way, not random. A definition is proposed and characterized in some ways. Other topics :
Prediction of the number of future new records. The earthquakes are well recorded, and people want safety against the strongest earthquake ever experienced. The problem is how often the record value will be broken. By new records the events are partitioned into intervals and a model of new records is developed for the prediction.
A distance between partitions of a finite set can be defined similarly to Hamming distance between binary codes. The distance between independent two random partitions can be used to characterize the random partition. Moreover the distance can be used to define a center of the random partitions. Hence a sampling distributions of the random partition can be constructed.
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