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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-02-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/3/152 |
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| Summary: | 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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| ISSN: | 2075-1680 |