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.