This paper studies the E-Bayesian (expectation of the Bayesian estimation) estimation of the parameter of Lomax distribution based on different loss functions. Under different loss functions, we calculate the Bayesian estimation of the parameter and then calculate the expectation of the estimated value to get the E-Bayesian estimation. To measure the estimated error, the E-MSE (expected mean squared error) is introduced. And the formulas of E-Bayesian estimation and E-MSE are given. By applying Markov Chain Monte Carlo technology, we analyze the performances of the proposed methods. Results are compared on the basis of E-MSE. Then, cases of samples in real data sets are presented for illustration. In order to test whether the Lomax distribution can be used in analyzing the datasets, Kolmogorov Smirnov tests are conducted. Using real data, we can get the maximum likelihood estimation at the same time and compare it with E-Bayesian estimation. At last, we get the results of the comparison between Bayesian and E-Bayesian estimation methods under three different loss functions.
翻译:本文研究了基于不同损失功能的Lomax分布参数的E-Bayesian(Bayesian估计)估计(Bayesian估计),根据不同的损失函数。在不同的损失函数下,我们计算Bayesian对参数的估计,然后计算估计值的预期值,以获得E-Bayesian估计值。为了测量估计误差,采用了E-Bayesian估计值(预期平均正方值误差)和E-MSE的公式。通过应用Markov 链子 Monte Carlo技术,我们分析了拟议方法的性能。结果根据E-MSE进行了比较。然后,对真实数据集中的样本案例进行了比较,以供参考。为了测试能否将Lamax分布值用于分析数据集, Kolmogorov Smirnov 测试正在进行。使用真实数据,我们可以在同一时间获得最大的可能性估计值,并与E-Bayesian估计值进行比较。最后,我们从三种不同的损失函数下获得Bayesian和E-Bayesian估计方法的比较结果。