基于随机过程因果关系的一种统计模型

Statistical Model Based on Random Process Causal Relation

基于随机过程所有随机作用因素与输出信号随机量之间因果关系的分析,建立了符合物理学量纲Π定理的无量纲幂函数模型。在最小度量单位的基础上,根据随机变量几何平均值定义,推导出该模型中所有随机变数服从以自然数n为自变量的对数正态分布律,并借助于光电传感器随机噪声信号不同层次随机变量的分析,以很高的精准度验证了随机变量服从对数正态分布律。

Based on the analysis of the causal relation between all random effect elements and output signal random variables in random process, a dimensionless power function model is es- tablished, which fits the physics dimension/7 theorem. On the basis of the smallest measure u- nits and the definition of random variable geometric mean, it is deduced that all random variables in this model obey the logarithmic normal distribution law, with natural number n as the independent variable. By means of analyzing the random variables in different levels of photoelectric sensor random noise signal, we verify with high precision that random variables obey logarithmic normal distribution law.