The Improved Zero Inflation Binomial Distribution Model And Its Applications

In the process of constructing counter model,the big difference among the count data will often encountered.When the variances are greater than the mathematical expectations,it is the presence of a discrete phenomenon.Due to the presence of a large number of zero values caused by the difference between the expectation and variance,that is,zero expansion will occur.For the processing of the data,the current selection is usually a discrete distribution model in line with the actual situation and the zero expansion structure combination,to construct an appropriate zero expansion discrete distribution model to deal with this problem.Because of the significant effects for the zero expansion structure to the zero phenomenons,zero-inflated Poisson model,zero-inflated negative binomial model and its extended forms,are widely used in industry,agriculture,insurance,environmental science,forest fires,traffic accident control and other fields.Focus on the above-mentioned structure of the model is that the value of the zero-crossing phenomenon analysis processing,the data distributions for the study have not been abundantly carried out.Firstly,based on the comprehensive profound analysis for the data distribution which will be studied in this paper,we found that there are only two mutually exclusive results,and it shows the typical characteristics of the binomial distribution.However,with further analysis on the study of data distribution,we found that in this data distribution,the mathematical expectation value is less than variance value,and it does not meet the prerequisites that the expectation of the binomial distribution should be greater than the variance.Therefore,we extend the traditional binomial model to more general forms.Through the introduction of a global divergence to reconstruct the improved binomial model,it can not only meet the characteristic that the expectation of the data structure is smaller than the variance,but also will be consistent with binomial distribution characteristics.Secondly,considering that the zero phenomenon exists in the object of this study,in this paper,we combine the zero-inflated structure with the improved binomial model to construct an improved zero expansion binomial model.So that it can solve the data from the excessive emissions with the phenomenon of the zero value problem and the problem of expectation less than variance of data.Following by maximum likelihood estimation and Newton iterative method,the optimal global adjustment divergence is introduced to increase its range of applications.Finally,based on empirical analysis on a set of actual emissions data,the AIC,BIC are used to test the goodness of fit of the model structure,and the cross-validation for the fitting results is tested.Experimental results show that the improved zero expansion binomial distribution can achieve better fitting effects;the AIC,BIC and LR values are less than the cases by the other zero expansion distribution models.It shows that the improved distribution model in the adaptability and robustness are strong practical significance and theoretical values.