On Posterior Properties of the Two Parameter Gamma Family of Distributions

被引：1

作者：

Ramos, Pedro L. ^{[1
]}

Dey, Dipak K. ^{[2
]}

Louzada, Francisco ^{[3
]}

Ramos, Eduardo ^{[3
]}

机构：

[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

来源：

ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS | 2021年 / 93卷

基金：

巴西圣保罗研究基金会;

关键词：

Gamma distribution; improper prior; objective prior; posterior property; FREQUENTIST VALIDITY; QUANTILES;

D O I：

10.1590/0001-3765202120190826

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页数：20

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