On Posterior Properties of the Two Parameter Gamma Family of Distributions

Author(s)

Ramos, Pedro L. ^[1] ; Dey, Dipak K. ^[2] ; Louzada, Francisco ^[3] ; Ramos, Eduardo ^[3]

Affiliation

^[1] Pontificia Univ Catolica Chile, Fac Matemat, Vicuna Mackenna 4860, Macul 7820436, Region Metropol - Chile

^[2] Univ Connecticut, Dept Stat, 215 Glenbrook Rd, U-4120, Storrs, CT 06269 - USA

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Anais da Academia Brasileira de Ciências; v. 93, n. 3 2021.
• Web of Science Citations: 0

Abstract

The gamma distribution has been extensively used in many areas of applications. In this paper, considering a Bayesian analysis we provide necessary and sufficient conditions to check whether or not improper priors Lead to proper posterior distributions. Further, we also discuss sufficient conditions to verify if the obtained posterior moments are finite. An interesting aspect of our findings are that one can check if the posterior is proper or improper and also if its posterior moments are finite by looking directly in the behavior of the proposed improper prior. To illustrate our proposed methodology these results are applied in different objective priors. (AU)

• FAPESP's process: 17/25971-0 - Statistical inference of complex systems
• Grantee: Pedro Luiz Ramos
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 19/27636-9 - Posteriori properties for Bayesian regression models and applications in large and complex industrial and medical data
• Grantee: Eduardo Ramos
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC