广义泊松分布是普通泊松分布的自然推广,克服均值与方差相等的局限性.在计数数据中, 常常会有多变量的情形,比如保险保单定价.因此文章考虑多元广义泊松分布的参数估计和假设检验问题, 针对共协方差多元广义泊松模型提出两种参数估计的方法,矩估计方法和极大似然估计方法,并比较两种方法的优劣性. 文章就多元广义泊松分布的假设检验问题,主要探讨了其退化检验及独立性检验,由于参数及变量较多, 运用似然比检验方法构造服从卡方分布的检验统计量.最后,运用多元广义泊松理论分析不同地区森林发生火灾的次数, 首先用文中提到的检验方法诊断数据是否可以用多元广义泊松分布,其次进行参数估计及实际问题的分析解释.

Generalized Poisson distribution is a natural generalization of the standard Poisson distribution. It overcomes the limitation that the mean is equal to the variance. In count data, there are multiple variables at usual, such as insurance policy pricing. This paper considers parameter estimation and hypothesis testing of multivariate generalized Poisson distribution. As to the total covariance multivariate generalized Poisson model, this paper proposes two parametric estimation methods, and compares the advantages and disadvantages of the methods. In terms of the hypothesis testing of multivariate generalized Poisson distribution, we mainly discuss the degradation test and independence test. Due to a lot of parameters and variables, the likelihood ratio test statistics is used with a Chi-square distribution. Finally, we use the multivariate generalized Poisson theory to analyze the number of forest fires in different regions. In this paper, we utilize the test method mentioned in the paper to diagnose whether the data can be used in multivariate generalized Poisson distribution, and then conduct the parametric estimation and the interpretation of the practical problem.