偏正态分布参数的贝叶斯估计  

Bayes Estimation of Partial Normal Distribution Parameters

作　　者：谭涛 吴黎军[1] TAN Tao;WU Li-jun(School of Mathematics and Systems Science,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《数学的实践与认识》2021年第16期181-188,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861064);自治区自然科学基金(2018D01C074)。

摘　　要：经典学派很注重已经出现的样本观察值,对于未观察到的样本不予考虑.贝叶斯学派很注重先验信息的收集、挖掘和加工,使它们数量化成先验分布,参与到统计推断中,以此提高统计推断的质量.研究了广义加权损失函数的贝叶斯估计,并且基于偏正态分布,建立了不同损失函数下的贝叶斯估计,并运用Matlab进行数值模拟,分别得到了偏正态分布的位置参数以及尺度参数与样本容量之间的关系图,由图比较了在同一损失函数下样本容量与各参数的贝叶斯估计之间的关系,并分析了不同损失函数下贝叶斯估计的差异性.The classical school pays much attention to using observations have not observed samples,samples will not be considered.Bayesian school pays much attention to the prior information collection,mining and processing,make them into the number of prior distribution,to participate in statistical inference,in order to improve the quality of statistical inference.This paper is based on normal distribution,establish estimates Bayesian under different loss functions,and the use of Matlab numerical simulation,obtained the position parameters of partial normal distribution as well as the relationship between map scale parameter and sample capacity,by compared the relationship between sample size and various parameters in the same loss function,and analyzes the difference between the estimated under different loss functions Bayesian.

关 键 词：偏正态分布 贝叶斯估计 广义加权损失函数 平方损失函数 指数损失函数 Esscher损失函数 

分 类 号：O212.8[理学—概率论与数理统计]