Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model

The Gompertz distribution has proven highly valuable in modeling human mortality rates and assessing the impacts of catastrophic events, such as plagues, financial crashes, and famines. Record data, which capture extreme values and critical trends, are particularly relevant for analyzing such phenom...

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Main Authors: Zoran Vidović, Liang Wang
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/14/3/152
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author Zoran Vidović
Liang Wang
author_facet Zoran Vidović
Liang Wang
author_sort Zoran Vidović
collection DOAJ
description The Gompertz distribution has proven highly valuable in modeling human mortality rates and assessing the impacts of catastrophic events, such as plagues, financial crashes, and famines. Record data, which capture extreme values and critical trends, are particularly relevant for analyzing such phenomena. In this study, we propose an objective Bayesian framework for estimating the parameters of the Gompertz distribution using record data. We analyze the performance of several objective priors, including the reference prior, Jeffreys’ prior, the maximal data information (MDI) prior, and probability matching priors. The suitability and properties of the resulting posterior distributions are systematically examined for each prior. A detailed simulation study is performed to assess the effectiveness of various estimators based on the performance criteria. To demonstrate the practical application of the methodology, it is applied to a real-world dataset. This study contributes to the field by providing a thorough comparative evaluation of objective priors and showcasing their impact and applicability in parameter estimation for Gompertz distribution based on record values.
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spelling doaj-art-d306dd1506304fa7a9fdebf9fd83bc2e2025-08-20T03:43:30ZengMDPI AGAxioms2075-16802025-02-0114315210.3390/axioms14030152Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz ModelZoran Vidović0Liang Wang1Faculty of Education, University of Belgrade, Kraljice Natalije 43, 11000 Belgrade, SerbiaSchool of Mathematics, Yunnan Normal University, Kunming 650500, ChinaThe Gompertz distribution has proven highly valuable in modeling human mortality rates and assessing the impacts of catastrophic events, such as plagues, financial crashes, and famines. Record data, which capture extreme values and critical trends, are particularly relevant for analyzing such phenomena. In this study, we propose an objective Bayesian framework for estimating the parameters of the Gompertz distribution using record data. We analyze the performance of several objective priors, including the reference prior, Jeffreys’ prior, the maximal data information (MDI) prior, and probability matching priors. The suitability and properties of the resulting posterior distributions are systematically examined for each prior. A detailed simulation study is performed to assess the effectiveness of various estimators based on the performance criteria. To demonstrate the practical application of the methodology, it is applied to a real-world dataset. This study contributes to the field by providing a thorough comparative evaluation of objective priors and showcasing their impact and applicability in parameter estimation for Gompertz distribution based on record values.https://www.mdpi.com/2075-1680/14/3/152Gompertz distributionmaximum likelihood estimatesobjective priorsproper posteriorsrecords
spellingShingle Zoran Vidović
Liang Wang
Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model
Axioms
Gompertz distribution
maximum likelihood estimates
objective priors
proper posteriors
records
title Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model
title_full Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model
title_fullStr Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model
title_full_unstemmed Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model
title_short Objective Posterior Analysis of <i>k</i>th Record Statistics in Gompertz Model
title_sort objective posterior analysis of i k i th record statistics in gompertz model
topic Gompertz distribution
maximum likelihood estimates
objective priors
proper posteriors
records
url https://www.mdpi.com/2075-1680/14/3/152
work_keys_str_mv AT zoranvidovic objectiveposterioranalysisofikithrecordstatisticsingompertzmodel
AT liangwang objectiveposterioranalysisofikithrecordstatisticsingompertzmodel