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AN IN-DEPTH REVIEW OF THE WEIBULL MODEL WITH A FOCUS ON VARIOUS PARAMETERIZATIONS

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dc.creatorYOLANDA MAGALY GĂ“MEZ OLMOS
dc.creatorDIEGO IGNACIO GALLARDO MATELUNA
dc.date2024
dc.date.accessioned2025-01-10T15:48:01Z
dc.date.available2025-01-10T15:48:01Z
dc.date.issued2024
dc.description.abstractTHE WEIBULL DISTRIBUTION IS A VERSATILE PROBABILITY DISTRIBUTION WIDELY APPLIED IN MODELING THE FAILURE TIMES OF OBJECTS OR SYSTEMS. ITS BEHAVIOR IS SHAPED BY TWO ESSENTIAL PARAMETERS: THE SHAPE PARAMETER AND THE SCALE PARAMETER. BY MANIPULATING THESE PARAMETERS, THE WEIBULL DISTRIBUTION ADEPTLY CAPTURES DIVERSE FAILURE PATTERNS OBSERVED IN REAL-WORLD SCENARIOS. THIS FLEXIBILITY AND BROAD APPLICABILITY MAKE IT AN INDISPENSABLE TOOL IN RELIABILITY ANALYSIS AND SURVIVAL MODELING. THIS MANUSCRIPT EXPLORES FIVE PARAMETERIZATIONS OF THE WEIBULL DISTRIBUTION, EACH BASED ON DIFFERENT MOMENTS, LIKE MEAN, QUANTILE, AND MODE. IT METICULOUSLY CHARACTERIZES EACH PARAMETERIZATION, INTRODUCING A NOVEL ONE BASED ON THE MODEL?S MODE, ALONG WITH ITS HAZARD AND SURVIVAL FUNCTIONS, SHEDDING LIGHT ON THEIR UNIQUE PROPERTIES. ADDITIONALLY, IT DELVES INTO THE INTERPRETATION OF REGRESSION COEFFICIENTS WHEN INCORPORATING REGRESSION STRUCTURES INTO THESE PARAMETERIZATIONS. IT IS ANALYTICALLY ESTABLISHED THAT ALL FIVE PARAMETERIZATIONS DEFINE THE SAME LOG-LIKELIHOOD FUNCTION, UNDERLINING THEIR EQUIVALENCE. THROUGH MONTE CARLO SIMULATION STUDIES, THE PERFORMANCES OF THESE PARAMETERIZATIONS ARE EVALUATED IN TERMS OF PARAMETER ESTIMATIONS AND RESIDUALS. THE MODELS ARE FURTHER APPLIED TO REAL-WORLD DATA, ILLUSTRATING THEIR EFFECTIVENESS IN ANALYZING MATERIAL FATIGUE LIFE AND SURVIVAL DATA. IN SUMMARY, THIS MANUSCRIPT PROVIDES A COMPREHENSIVE EXPLORATION OF THE WEIBULL DISTRIBUTION AND ITS VARIOUS PARAMETERIZATIONS. IT OFFERS VALUABLE INSIGHTS INTO THEIR APPLICATIONS AND IMPLICATIONS IN MODELING FAILURE TIMES, WITH POTENTIAL CONTRIBUTIONS TO DIVERSE FIELDS REQUIRING RELIABILITY AND SURVIVAL ANALYSIS.
dc.formatapplication/pdf
dc.identifier.doi10.3390/math12010056
dc.identifier.issn2227-7390
dc.identifier.urihttps://repositorio.ubiobio.cl/handle/123456789/13708
dc.languagespa
dc.publisherMATHEMATICS
dc.relation.uri10.3390/math12010056
dc.rightsPUBLICADA
dc.subjectWeibull distribution
dc.subjectsurvival modeling
dc.subjectreparameterization
dc.subjectregression models
dc.titleAN IN-DEPTH REVIEW OF THE WEIBULL MODEL WITH A FOCUS ON VARIOUS PARAMETERIZATIONS
dc.typeARTĂŤCULO DE REVISIĂ“N
dspace.entity.typePublication
ubb.EstadoPUBLICADA
ubb.Otra ReparticionDEPARTAMENTO DE ESTADISTICA
ubb.Otra ReparticionDEPARTAMENTO DE ESTADISTICA
ubb.SedeCONCEPCIĂ“N
ubb.SedeCONCEPCIĂ“N
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