基于一元线性回归的可能性分布构造方法研究

The Construction Method of Possibility Distribution Based on One-Variable Linear Regression

针对近似服从一条直线或曲线的一系列离散数据的可能性分布构造问题,以一元线性回归知识为理论基础,提出了基于一元线性回归的可能性分布构造方法.首先,根据离散数据的分布特点,选出线性或非线性的最优模型.然后,利用最小二乘法估计最优模型中的未知参数,进而求出回归方程;对回归方程中的参数进行回归效果的显著性检验,将回归方程转化为可能性分布函数.最后结合两个实例作了具体分析.实验结果表明:此构造可能性分布的方法能够贴切地对认知不确定性进行描述,减小了与真实分布的差异.

For the possibility distribution construction of a series of discrete data approximate to a straight line or curve, a construction method of possibility distribution based on one-variable linear regression was prop- osed. Firstly, optimal model of linear or nonlinear was chosen according to distribution characteristics of dis- crete data. Unknown parameters in optimal model were estimated by the least squares method and regression equation was obtained. Then the parameters of regression equation were carried on significance testing of re- gression effect and regression equation was transformed into possibility distribution function. Finally, two cas- es were made concrete analysis, and the experimental results show that the proposed method can describe cog- nitive uncertainty information appropriately, and decrease the difference of this possibility distribution and real distribution.