In this paper, we study E-Bayesian (expected value of Bayesian estimation) estimation of the parameters of the Lomax distribution based on various loss functions. Under various loss functions, we compute Bayesian estimates of parameters, compute expected values of estimates, and obtain E-Bayesian estimates. E-MSE (expected mean squared error) is introduced to measure the estimation error. And the formulas of E-Bayes estimation and E-MSE are given. We analyze the performance of the proposed method by applying the Markov Chain Monte Carlo technique. Results are compared based on E-MSE. A sample case from a real dataset is then presented for illustration. A Kolmogorov-Smirnov test is performed to test whether the Lomax distribution can be used to analyze the dataset. Using real data, you can simultaneously obtain a maximum likelihood estimate and compare it with the E-Bayesian estimate. Finally, we get the comparative results of the Bayesian estimation method and his E-Bayesian estimation method under three different loss functions.
