Project/Area Number  09640266 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Osaka University 
Principal Investigator 
GOTO Masashi Professor, Department/Division of Ingormatics and Mahtematical Science, Graduate School of Engineering Sciences, Osaka University, 大学院・基礎工学研究科, 教授 (00273615)

CoInvestigator(Kenkyūbuntansha) 
稲垣 宣生 大阪大学, 大学院・基礎工学研究科, 教授 (10000184)
TANIGUCHI Masanobu Associated Professor.Department/Division of Informatics and Mathematical Science, 大学院・基礎工学研究科, 助教授 (00116625)
SHIRAHATA Shingo Professor, Department/Division of Informatics and Mathematical Sciences, Graduat, 大学院・基礎工学研究科, 教授 (10037294)
衛藤 俊寿 富士通大分ソフトウェア, ラボラトリ統計解析, 主任
OHTAKI Megu Professor, Department of Environmetrics and Biometrics, Research Institute for R, 原爆放射能医学研究所, 教授 (20110463)
SAKAMOTO Wataru Assistant.Department/Division of Informatics and Mathematical Sciences, Graduate, 大学院・基礎工学研究科, 助手 (70304029)
衞藤 俊寿 富士通大分ソウトウェア, ラポラトリ 統計解析, 主任(研究員)
ETO Toshihisa hed researchor.Fujitu Oita Sobteween Lab.

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1998 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Power transformation / Powernormal distribution / Grouped observations / Doublepower transformations / Transformation Diagnosis / AGE / Bivariate powernormal distribution / Regression diagnosis / ベキ変換 / ベキ正規分布 / 2変量ベキ正規分布 / 対数変換 / 回帰診断 / 変換グラフィクス / ACE / 2重ベキ変換 
Research Abstract 
The purposes of the project are to research some types and methods of parametric and nonparametric transformations of data, to evaluate performances for practical uses, and to develop their extensions. In the project research, we could obtain the following results and some productive findings : We have proposed three extended powertransformations, namely Doublepower Normal Transformation (DPNT). Doublepower Additive Transformation (DPAT), and Doublepower Weighted Transformation (DPWT). Further, we evaluated performances of the proposed transformations by applying to some examples cited in literatures and conducting simulations experiments. These transformations have shown better performances than ordinary power transformation, in normality and homogeneity of observation, and additivity of model. A modified power transformation was proposed to ordinary power transformation. This transformation is completely equal to identity transformation when transformation of data is not necessary
… More
. Incidentally, the ordinary power transformation was nearly equal to identity transformation in such case. We have shown inference approach of the powernormal distribution based on grouped observations and their extensive applications. These results was useful in analyses of practical data, especially biomedical and behaviormetric data. Further, the inforence procedure was extended to case which both grouped and ungrouped observations were included. Nonparametric transformation ACE were extended to combine it with SIR and some performances of the approach was evaluated. The computer program of the approach was also developed and produced to the research on many follows. As a control of the power normal distribution, we have investigated loggamma distribution and evaluated some its performances relative to the power normal distribution of fitting to some practical data, and further have shown extensive applications to medical field. We have investigated possibility of transforming qualitative data to their quantitative forms by using the power transformation. Particularly, we evaluated the appropriateness of logtransformation to data which had Poisson distribution. Less
