Research of Statistical Transformation Methodology

该项目的目的是研究数据的参数和非参数转换的一些类型和方法，评估实际使用的性能，并开发其扩展。在课题研究中，我们取得了以下成果和一些富有成效的发现：提出了三种扩展幂变换，即双幂正态变换（DPNT）。双幂加法变换（DPAT）和双幂加权变换（DPWT）。此外，我们通过应用于文献中引用的一些例子和进行模拟实验，评估所提出的转换的性能。这些变换在观测的正态性、齐次性和模型的可加性方面都比普通幂变换有更好的表现，提出了一种改进的幂变换.当不需要数据变换时，这种变换完全等同于恒等变换 ...更多信息 .顺便说一下，在这种情况下，普通的幂变换几乎等于恒等变换，我们给出了基于分组观测的幂正态分布的推断方法及其广泛的应用。这些结果对实际数据，特别是生物医学和行为测量数据的分析是有用的。进一步将信息处理方法推广到既包含分组观测值又包含未分组观测值的情况，并将非参数变换ACE推广到与SIR相结合的联合收割机，并对该方法的性能进行了评价。本文还编制了该方法的计算机程序，并对以下几个方面进行了研究：作为幂正态分布的控制，我们研究了对数伽玛分布，并评价了它相对于幂正态分布拟合实际数据的一些性能，并在医学领域得到了广泛的应用。我们研究了通过以下方式将定性数据转化为定量形式的可能性：利用能量转换。特别地，我们评估了对数转换对具有泊松分布的数据的适当性。少

The purposes of the project are to research some types and methods of parametric and non-parametric 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 power-transformations, namely Double-power Normal Transformation (DPNT). Double-power Additive Transformation (DPAT), and Double-power 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 power-normal 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.Non-parametric 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 log-gamma 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 log-transformation to data which had Poisson distribution. Less