Study On The Application Of Generalized Poisson Distribution

With the study of the distribution for a type of discrete samples truncated data with aggregation, we improved Truncated Poisson model which cannot fit such data accurately. In this paper, we put forward a new type of Mixture truncated Poisson model which fitting the data better.Besides, this new Poisson mode is a generalized model of Truncated Poisson, it could also be used for the data of Truncated Poisson and fit better. The paper focuses on Left Truncated Poisson mixed, mixed double truncated Poisson distribution and the new mixed left-truncated Poisson distribution. And their likelihood function,logarithmic likelihood function and the partial derivative of the logarithmic likelihood function were given respectively. Moreover, we compared the results of fitting data of such models where the parameters were estimated by maximum likelihood method. Furthermore using MATLAB fsolve function to solve the root of partial derivative equation of logarithmic likelihood function. Using 2test to test the result of each model. And utilizing the likelihood ratio test is a great way for the null hypothesis, which could discuss simple test problems. Finally, according to the actual context of the data, given the prospect of a new model in real life. Finally, According to the background of the actual data, this paper gives the application prospects of the new model in our life.