Algunas caracterizaciones del Proceso Poisson Mixto

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dc.contributor.advisorJiménez Moscoso, José Alfredospa
dc.contributor.authorPalomino Velandia, Gerson Yahirspa
dc.contributor.orcidPalomino Velandia, Gerson Yahir [000000018043050X]
dc.contributor.orcidJiménez Moscoso, José Alfredo [0000000223912809]
dc.date.accessioned2025-11-28T13:37:46Z
dc.date.available2025-11-28T13:37:46Z
dc.date.issued2025-08
dc.descriptionilustraciones, gráficas, tablasspa
dc.description.abstractEn esta tesis se estudia el Proceso Poisson Mixto (PPM ), mediante un compilado de sus propiedades y caracterizaciones más relevantes. Como caso particular, se analiza el proceso de Hofmann, definido por Hofmann (1955) y estudiado posteriormente por Walhin (2000) y Jiménez-Moscoso (2013), generando una nueva caracterización a través de las intensidades de transición. Como resultado de este trabajo, se obtuvieron diversas recurrencias y propiedades del Proceso Poisson Mixto que permiten, entre otras cosas, recuperar como casos particulares algunos de los procesos de conteo más conocidos en la literatura, así como otros nuevos, entre los cuales se encuentran los procesos Poisson-beta transformado, Poisson-beta exponencial, Poisson-chi cuadrado no central, Poisson-Lévy, Poisson-Nakagami, Poisson-Rayleigh, Poisson-semi-normal y Poisson-Weibull. Asimismo, se obtuvo una expresión para el momento de orden r de las distribuciones de Hadwiger, Riebesell y Riebesell generalizada. Estas expresiones, junto con otras ya conocidas, se utilizaron para encontrar la distribución del Proceso Poisson Mixto (PPM). También se caracteriza al PPM como un proceso de nacimiento puro, a partir del análisis de sus intensidades de transición, lo que permite derivar propiedades relevantes del modelo. Finalmente, se derivaron las distribuciones de los procesos Pólya-Aeppli y Poisson-Pascal como casos particulares del Proceso Poisson Mixto, al considerar variables de estructura continua con distribuciones Riebesell y Riebesell generalizada, respectivamente. Cabe destacar que estos procesos, hasta ahora, solo habían sido presentados en la literatura como procesos Poisson compuestos. (Texto tomado de la fuente).spa
dc.description.abstractThis thesis studies the Mixed Poisson Process (MPP) by compiling its most relevant properties and characterizations. As a particular case, it examines the Hofmann process, originally defined by Hofmann (1955) and later studied by Walhin (2000) and Jiménez-Moscoso (2013), leading to a new characterization based on transition intensities. As a result of this work, several recurrence relations and properties of the Mixed Poisson Process were derived. These results make it possible to recover several well-known counting processes from the literature as particular cases, as well as to introduce new processes, including the Poisson-beta transformed, Poisson-beta exponential, Poisson–non-central chi-squared, Poisson-Lévy, Poisson-Nakagami, Poisson-Rayleigh, Poisson–semi-normal, and Poisson-Weibull processes. In addition, an expression for the r-th moment was obtained for the Hadwiger, Riebesell, and generalized Riebesell distributions. These results, together with existing expressions for other probability distributions, were used to derive the distribution of the MPP. The MPP is also characterized as a pure birth process, based on the analysis of its transition intensities, which allows for the derivation of relevant properties of the model. Finally, the distributions of the Pólya-Aeppli and Poisson-Pascal processes were obtained as particular cases of the Mixed Poisson Process, using continuous structure variables following Riebesell and generalized Riebesell distributions, respectively. Notably, these processes had previously only been presented in the literature as compound Poisson processes.eng
dc.description.degreelevelMaestríaspa
dc.description.degreenameMagíster en Ciencias - Estadísticaspa
dc.format.extent160 páginasspa
dc.format.mimetypeapplication/pdf
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/89158
dc.language.isospa
dc.publisherUniversidad Nacional de Colombiaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotáspa
dc.publisher.departmentDepartamento de Estadísticaspa
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.placeBogotá, Colombiaspa
dc.publisher.programBogotá - Ciencias - Maestría en Ciencias - Estadísticaspa
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.rights.licenseReconocimiento 4.0 Internacional
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510 - Matemáticas::511 - Principios generales de las matemáticasspa
dc.subject.ddc510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasspa
dc.subject.proposalProceso Poisson Mixtospa
dc.subject.proposalProceso Poissonspa
dc.subject.proposalProceso de Hofmannspa
dc.subject.proposalProceso de conteospa
dc.subject.proposalPoisson processeng
dc.subject.proposalMixed Poisson processeng
dc.subject.proposalHofmann processeng
dc.subject.proposalCounting processeng
dc.subject.wikidatadistribución de probabilidadspa
dc.subject.wikidataprobability distributioneng
dc.subject.wikidataproceso estocásticospa
dc.subject.wikidatastochastic processeng
dc.subject.wikidatateoría de la probabilidadspa
dc.subject.wikidataprobability theoryeng
dc.titleAlgunas caracterizaciones del Proceso Poisson Mixtospa
dc.title.translatedSome characterizations of the Mixed Poisson Processeng
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdcc
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
dc.type.driverinfo:eu-repo/semantics/masterThesis
dc.type.redcolhttp://purl.org/redcol/resource_type/TM
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dcterms.audience.professionaldevelopmentEstudiantesspa
dcterms.audience.professionaldevelopmentInvestigadoresspa
dcterms.audience.professionaldevelopmentMaestrosspa
dcterms.audience.professionaldevelopmentPúblico generalspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2

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