Pareto分布形状参数的简单贝叶斯估计

A simple Bayesian estimation of the shape parameter of Pareto distribution

针对Pareto分布,在尺度参数已知、先验信息为某一固定时刻分布函数及其标准差的估计值的情况下,参考Kaminskiy等提出的简单贝叶斯估计过程,借助缺一交叉验证法以及核密度估计法,研究了形状参数的简单贝叶斯估计.基于上述先验信息,在估计过程中构造了Pareto分布形状参数的先验与后验概率密度、先验与后验点估计,并给出了在给定任意时刻分布函数及其标准差的先验与后验估计.最后通过一个数值例子说明了这种估计方法,并对灵敏度进行了定量分析.

A simple Bayesian estimation of the shape parameter of Pareto distribution is studied referring the simple procedure of Bayesian estimation proposed by Kaminskiy et al and with the help of the method of leave-one-out cross-validation and kernel density estimator, when the scale parameter of Pareto distribution is known and the prior information is the estimates of distribution function and its standard deviation. Based on the above prior information, the procedure allows constructing the prior and posterior density, the prior and posterior point estimates of the shape parameter of Pareto distribution, as well as the prior and posterior estimates of distribution function and its standard deviation at any given time. Finally, a numeric example is discussed as an illustration, and sensitivity analysis is also studied by quantity method.