Bayesian analysis for the Lomax model using noninformative priors. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: He, Daojiang; Sun, Dongchu; Zhu, Qing
• Is Part Of: Statistical theory and related fields. Volume 7:Issue 1(2023)
• Page Start: 61
• Page End: 68
• Publication Date: 2023-01-02
• Subjects: Lomax model -- probability matching priors -- MDI prior -- Jeffreys prior -- reference priors -- posterior propriety; Statistics -- Periodicals; Statistics; Periodicals; Electronic journals; 001.422
• DOI: 10.1080/24754269.2022.2133466
• Languages: English
• ISSNs: 2475-4269

Abstract

Abstract : The Lomax distribution is an important member in the distribution family. In this paper, we systematically develop an objective Bayesian analysis of data from a Lomax distribution. Noninformative priors, including probability matching priors, the maximal data information (MDI) prior, Jeffreys prior and reference priors, are derived. The propriety of the posterior under each prior is subsequently validated. It is revealed that the MDI prior and one of the reference priors yield improper posteriors, and the other reference prior is a second-order probability matching prior. A simulation study is conducted to assess the frequentist performance of the proposed Bayesian approach. Finally, this approach along with the bootstrap method is applied to a real data set.