泊松分布下的非线性拟合

对一数据涨落服从泊松概率分布的实验数据组进行拟合,如果拟合函数是非线性的,常常只能采用某些近似方法。近似性之一,表现在将拟合函数线性化,或者采用某种参数寻优的方法。近似性之二,则是将泊松问题近似地看作高斯分布问题。本文从最大或然法出发,对两类不同概率分布情况下的曲线拟合进行了比较,给出了对泊松分布问题更严格的求解途径。对于特殊的非线性拟合函数y(x)=ae~(bx~N),直接给出了迭代解。本文对曲线拟合的“面积亏损”问题,也进行了讨论。

Nonlinear Fitting in the Case of the Poisson Distribution

To fit a set of experiment data,of which the fluctuation obeys the Poisson probability distribution,if the fitting function is a nonlinear one,in general,only some approximate methods can be used.One of the approximations is to linearize the nonlinear fitting function,or to take some method of parameter search.The second is to regard the Poisson distribution as a Gaussian distribution approximately.In this paper,after comparing the curve fitting in the environment of the Poisson distribution with that of the Gaussian distribution from the method of maximum probability,a more accurate nonlinear fitting method in the case of the Poisson distribution is given.As for a special nonlinear functions of y(x)= a * exp(bxn),an exact resolution is directly obtained.The sensitive problem,i.e.the "area deficient under a curve" in the curve fitting,is also discussed.