泊松分布下线性多重回归问题

对一实验数据组进行线性多重回归,如果数据的涨落服从泊松概率分布,常用方法不能给出准确的解。一般地,是假设各泊松分布的形状近似于高斯分布,给出近似解。因此,也存在着人所共知的拟合曲线下的面积亏损问题。本文从最大或然法出发,不加任何假设,严格推导了求解泊松分布线性多重回归的一种方法。按这一方法,“面积亏损”问题在计算精度范围内也得到彻底解决。

Mutiple Linear Regression Based on the Poisson Distribution

When the mutiple linear regression is carried out for a set of experimental data,if the statistical fluctuations of the data obey the Poisson probability distribution,the methods most in use can not be used to give the accurate solution.In general,it is assumed that the shape of each Poisson distribution is similar to that of the Gaussian distribution and then an approximate solution may be found.But in this way,the "area deficient under a peak for the Poisson distribution" is produced.In this paper,a new strict method for solving the mutiple linear regression in the case of the Poisson distribution is given from the maximum likelihood method and without any hypothesis being added.By means of this method,the problem of the "area deficiency" is also completely solved.