  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.
