熵损失函数下的零截尾泊松分布的Bayes估计

发布时间：2018-04-13 20:19

本文选题：零截尾泊松分布 + Bayes估计　；参考：《吉林大学》2017年硕士论文

【摘要】：零截尾泊松分布被David和Johnson(1952)首次提出,引起了众多学者的关注和重视,并且在医学和生物科学等领域得到广泛的应用.该分布能够很好的拟合样本中计数取值至少为一次的计数数据.很多学者讨论了零截尾泊松分布的参数估计和性质及零截尾泊松回归模型的应用,但在不同损失函数下对零截尾泊松分布参数的Bayes估计研究则比较少见.本文在研究零截尾泊松分布参数估计的问题上,首先推导出了以Gamma分布为先验分布时,熵损失函数下的零截尾泊松分布参数的Bayes估计,并探讨了其容许性的问题.其次通过Monte Carlo数值模拟方法,将其与极大似然估计和在平方损失下的零截尾泊松分布的Bayes估计进行比较,得出在熵损失函数下参数估计的效果较好,且精度较高的结论.
[Abstract]:Zero Truncated Poisson distribution by David and Johnson (1952) proposed for the first time, attracted the attention of many scholars and attention, and has been widely used in medical and biological sciences. This distribution can well fit the sample counting value of at least one count data. Many scholars have discussed the application of zero Truncated Poisson distribution the parameter estimation and properties and zero Truncated Poisson regression model, but under different loss functions for Bayes parameter estimation of zero Truncated Poisson distribution is relatively rare. In this paper the study on the parameter estimation of zero Truncated Poisson distribution problem, firstly deduced with Gamma distribution as the prior distribution, estimation under entropy loss function zero Truncated Poisson distribution parameter Bayes, and discuss its admissibility problem. By using the Monte Carlo numerical simulation method, the maximum likelihood estimation and the zero section under the square loss The Bayes estimation of the tail Poisson distribution is compared. It is concluded that the estimation of parameters is better and the accuracy is higher under the entropy loss function.

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.8

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