The E-Bayesian Estimation and its E-MSE of Lomax distribution under different loss functions

TL;DR

This paper introduces the E-Bayesian estimation method for Lomax distribution parameters, calculates E-MSE, and compares its performance with traditional Bayesian methods using real data and MCMC techniques.

Contribution

It develops formulas for E-Bayesian estimation and E-MSE under various loss functions and applies MCMC to analyze their performance on real datasets.

Findings

E-Bayesian estimation outperforms traditional Bayesian estimation in E-MSE.

The proposed methods are validated using real data and Kolmogorov-Smirnov tests.

Comparison shows differences under various loss functions.

Abstract

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.