Maximum Likelihood Estimation Of Parameters For Bivariate Poisson Disdribution Population Under The Order Restriction

The properties and flexibility of the bivariate Poisson distribution have been studied in many literatures at home and abroad.There are many ways to generate the bivariate Poisson distribution.Scholars s.Kocherlakota and k.Kocherlakota proposed a method that is most commonly used,namely the three-variable reduction method.According to this method,the probability density function of the two-variable Poisson distribution is calculated.This paper mainly studies the maximum likelihood estimation and application of bivariate Poisson distribution parameters.Firstly,the maximum likelihood estimation problem of bivariate Poisson distribution parameters is studied.The Newton iteration method was used to solve the three unknown parameters.The moment estimation of the calculated parameters was substituted as the initial iterative value,and the real data of the accident times of 122 dispatchers in two different continuous time periods were substituted with MATLAB language to solve the maximum likelihood estimation of the parameters.Secondly,operator number of accidents,for example,a random sample of ten different areas as ten different overall,requires the risk of the cause of the accident from the work environment itself exists,personal and impersonal reasons three aspects influencing factors to consider,requests can be controlled in a certain range,minimize accidents,the parameters of probability density function and constraint conditions.By using PAVA algorithm,the maximum likelihood estimation that meets the conditions is obtained,and the minimum value of accident rate is obtained by comparison.Finally,the bivariate Com-Poisson distribution is obtained by expanding the bivariate Poisson distribution.To satisfy data dispersion,the bivariate Poisson distribution can no longer fully meet the conditions,so the bivariate Com-Poisson distribution is adopted to model the actual data.When the parameters of the bivariate Com-Poisson distribution take a specific value,it contains three special distributions,which are the bivariate Poisson distribution,the bivariate Bernoulli distribution and the bivariate geometric distribution.This part mainly considers the maximum likelihood estimation of the bivariate Com-Poisson distribution parameter,and uses MATLAB language to substitute the real data of the accident times of 122 dispatchers in two different continuous time periods,and finally obtains the estimated value.