零一膨胀几何分布的统计分析及应用

Statistical analysis and application of zero-and-one-inflated geometric distribution

研究了0−1膨胀几何分布模型,构造隐变量的条件分布,并设计抽样算法。在数据扩充的基础上,运用极大似然估计、期望极大(expectation maximization,EM)算法及贝叶斯方法对模型参数进行估计。设定不同的样本量和参数真值,通过数值模拟对上述方法进行性能评估。最后,对1994年美国底特律交通事故死亡数据集进行分析,研究表明,0−1膨胀几何分布模型能够较好地对该数据集进行拟合。

Zero-and-one-inflated geometric distribution model was investigated,the conditional distribution of latent variables were constructed,and a sampling algorithm was designed.On the basis of data expansion,the maximum likelihood estimation,expectation maximization(EM)algorithm and Bayesian method were employed to estimate the model parameters.Different sample sizes and parameter true values were setted,and the performance of these methods were evaluated through numerical simulations.Finally,the Detroit traffic accident deaths dataset in 1994 of United States were analyzed,the results indicate that zero-and-one-inflated geometric distribution model can fit the dataset better.