Power-law distribution in pieces: a semi-parametric approach with change point detection

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dc.contributor.authorRamos, Pedro L.
dc.contributor.authorJerez-Lillo, Nixon
dc.contributor.authorSegovia, Francisco A.
dc.contributor.authorEgbon, Osafu A.
dc.contributor.authorLouzada, Francisco
dc.date.accessioned2025-01-20T17:11:17Z
dc.date.available2025-01-20T17:11:17Z
dc.date.issued2024
dc.description.abstractPiecewise models play a crucial role in statistical analysis as they allow the same pattern to be adjusted over different regions of the data, achieving a higher quality of fit than would be obtained by fitting them all at once. The standard piecewise linear distribution assumes that the hazard rate is constant between each change point. However, this assumption may be unrealistic in many applications. To address this issue, we introduce a piecewise distribution based on the power-law model. The proposed semi-parametric distribution boasts excellent properties and features a non-constant hazard function between change points. We discuss parameter estimates using the maximum likelihood estimators (MLEs), which yield closed-form expressions for the estimators and the Fisher information matrix for both complete and randomly censored data. Since MLEs can be biased for small samples, we derived bias-corrected MLEs that are unbiased up to the second order and also have closed-form expressions. We consider a profiled MLE approach to estimate change points and construct a hypothesis test to determine the number of change points. We apply our proposed model to analyze the survival pattern of monarchs in the Pharaoh dynasties. Our results indicate that the piecewise power-law distribution fits the data well, suggesting that the lifespans of pharaonic monarchs exhibit varied survival patterns.
dc.fuente.origenWOS
dc.identifier.doi10.1007/s11222-023-10336-x
dc.identifier.eissn1573-1375
dc.identifier.issn0960-3174
dc.identifier.urihttps://doi.org/10.1007/s11222-023-10336-x
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/91172
dc.identifier.wosidWOS:001096038100001
dc.issue.numero1
dc.language.isoen
dc.revistaStatistics and computing
dc.rightsacceso restringido
dc.subjectPower-law
dc.subjectPiecewise model
dc.subjectChange points
dc.subjectPharaoh dynasties
dc.titlePower-law distribution in pieces: a semi-parametric approach with change point detection
dc.typeartículo
dc.volumen34
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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