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，评估实际应用的性能，并发展其扩展。在项目研究中，我们得到了以下结果和一些富有成效的发现：我们提出了三种扩展的幂变换，即双幂正态变换（DPNT）。双功率加性变换（DPAT）和双功率加权变换（DPWT）。此外，我们通过应用文献中引用的一些例子并进行模拟实验来评估所提出的变换的性能。这些变换在观测值的正态性、均匀性和模型的可加性方面都表现出比普通幂变换更好的性能。在普通功率变换的基础上，提出了一种改进的功率变换。当不需要对数据进行变换时，这种变换完全等于恒等变换……更多。顺便提一下，在这种情况下，普通的幂变换几乎等于恒等变换。给出了基于分组观测的幂正态分布的推理方法及其广泛应用。这些结果在分析实际数据，特别是生物医学和行为测量数据时是有用的。此外，将参考程序扩展到包括分组和非分组观察结果的情况。将非参数变换ACE扩展为与SIR相结合的方法，并对该方法的一些性能进行了评价。该方法的计算机程序也被开发和制作用于许多后续研究。作为功率正态分布的控制，我们研究了对数-伽马分布，并对一些实际数据进行了拟合，评价了它相对于功率正态分布的一些性能，并进一步在医学领域显示出广泛的应用。探讨了利用幂变换将定性数据转化为定量数据的可能性。特别地，我们评价了对数变换对泊松分布数据的适宜性。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