Mlinex损失函数下反向帕累托分布形状参数的Bayes估计

Bayes Estimates of Shape Parameters of Reverse Pareto Distribution under Mlinex Loss Function

文章研究了Mlinex损失函数下反向帕累托分布的参数估计问题。在已知反向帕累托分布位置参数的情况下,给出形状参数的五种估计方法:极大似然估计、最大后验估计、经典Bayes估计、多层Bayes估计、E-Bayes估计,并推导出相应估计方法下的具体表达式。利用MC方法在R软件下进行数值模拟,对比模拟数据确定了参数估计的最优环境,并验证了估计方法的合理性和估计结果的准确性与稳健性,得到了E-Bayes估计为最优估计方法的结论;最后利用最优估计方法对实例进行数据拟合,确定了新疆县市级城市的人均城市道路面积可以利用反向帕累托分布近似拟合,并结合最终数据给出了相应的数据分析。

In this paper,the parameter estimation problem of inverted Pareto distribution under Mlinex loss function is studied.In the case of knowing the positional parameters of the inverted Pareto distribution,five estimation methods for the shape parameters are given:maximum likelihood estimation,maximum posterior estimation,classical Bayes estimation,multilayer Bayes estimation,E-Bayes estimation,and the specific expressions under the corresponding estimation methods are derived.The MC method is used to carry out numerical simulation under R software,the optimal environment for parameter estimation is determined by comparing the simulation data,and the rationality of the estimation method and the accuracy and robustness of the estimation results are verified,the conclusion that E-Bayes estimation is the optimal estimation method is obtained.Finally,the optimal estimation method is used to fit the data of the examples,and it is determined that the per capita urban road area of Xinjiang counties and cities can be approximated by using the reverse Pareto distribution,and the corresponding data analysis is given in combination with the final data.