基于Beta-Binomial的膨胀分布推广及置信区间构造

Expansion Distribution Promotion and Confidence Interval Construction Based on Beta-Binomial

膨胀分布的推广及参数估计一直是计数数据分析的热点问题.第一,对0膨胀和0-1膨胀分布进行推广,构建0膨胀Beta-Binomial分布和0-1膨胀BetaBinomial 分布;第二,基于极大似然估计法对参数进行点估计,并采用不动点迭代修正EM算法中的M步,使EM算法更适用于这两类分布参数的估计;第三,对参数进行区间估计,通过Fisher信息矩阵计算参数方差,进而构造参数的置信区间;第四,选择拟合效果相对最优的分布,结合AIC准则和BIC准则给出不同拟合分布的遴选方法.最后,通过数值模拟和实例研究发现,ZIBB分布与ZOIBB分布的数据结构存在明显差异,但都在小样本量下的拟合效果最优.

The promotion of expansion distribution and parameter estimation have always been hot issues in counting data analysis.First,generalize the 0 expansion and 0-1 expansion distributions,and construct the 0 expansion Beta-Binomial distribution and the 0-1 expansion Beta-Binomial distribution;Second,point estimation of parameters based on the maximum likelihood estimation method,and using fixed point iteration to modify the M steps in the EM algorithm,making the EM algorithm more suitable for the estimation of these two types of distribution parameters;Third,perform interval estimation on the parameters,calculate the parameter variance through the Fisher information matrix,and then construct the confidence interval of the parameters;Fourth,select the distribution with the relatively optimal fitting effect,and combine the AIC criterion and the BIC criterion to give a selection method for different fitted distributions.Finally,through numerical simulation and case studies,it is found that the data structure of the ZIBB distribution and the ZIBB distribution are significantly different,but both have the best fitting effect under a small sample size.