选择模型的理论扩展分析

Analysis on theory of selective model

选择模型为解释指数律、幂律的成因提供了基于偏好的概率分析方法.通过对选择试验的研究,在视野规律和选项分布之间导出了一对变换,称其为偏序变换.对偏序变换连续化,导出了对应的连续变换.仿照离散分布,定义了连续分布的比较函数,并沟通了离散和连续分布的伴随关系.通过选择模型,对幂律访问现象进行了仿真.选择理论对于复杂巨系统和社会行为的研究具有较重要的借鉴作用,可扩展统计物理学和概率论的理论基础.

Selective model provided a way to explain the generation of index law and power law on the basis of preferential probability analysis. A transformation formula between the selective scope rule and selective distribution was deduced through the research on preferential trials. It was named as preferential transformation, which offered a mean to study the rule of monotone distributions. A corresponding continuous transformation can be deduced by the preferential transformation for analyzing probability density function. Compared with the discrete distribution, we defined a comparison function for continuous distribution, and pointed out the relationship between the discrete distribution and continuous distribution. Through selective model, we simulated and analyzed the power law phenomena. Selective theory was important to the research on huge complex system and social behavior. It could also expand the foundation of statistical physics and probability theory.