{"id":{"repo_id":"unr","oai_identifier":"oai:scholarwolf.unr.edu:11714/11553"},"canonical_url":"https://search.dev.ndltd.org/etd/unr/oai:scholarwolf.unr.edu:11714/11553","repository":{"repo_id":"unr","name":"University of Nevada - Reno","base_url":"https://scholarwolf.unr.edu/server/oai/request"},"display":{"title":"Flexible Statistical Models for Imprecise and Uncertain Data: A New Generalization Approach","abstract":"We propose a general framework for extending any probability distribution ν to an absolutely continuous distribution with density g(y) =ν(y + A)/|A|, where A is any bounded measurable set of size |A|. This generalized distribution allows the model to adapt to data characteristics that the original (or \"base\") distribution ν may not fully capture. We show that this generalized distribution corresponds to that of X + U, where X ~ ν and U is uniformly distributed over A, with X and U independent. This convolution-based framework enables the construction of new probability distributions by introducing additive uniform noise to a known parent distribution. Motivated by practical considerations such asimprecise measurements, data contamination, and truncation, the framework offers a flexible and analytically tractable approach to modeling distributional uncertainty. The key idea - representing the observed variable as the sum of a latent signal and bounded noise - produces generalized distributions that preserve the interpretability of the parent model while accommodating real-world imperfections. This dissertation develops the theoretical foundations of the proposed construction, examines its properties, and explores its potential applications. In particular, we apply the framework to construct a new class of Extended Laplace (EL) distributions, designed to model Laplace data affected by independent uniform errors. We derive the fundamental properties of this EL distribution, propose a robust likelihood-based estimation method, and validate its performance through simulation studies. Applications in finance illustrate the EL model's effectiveness in handling real-world data with inherent uncertainties. In the multivariate setting, we also develop a bivariate Bear-Claw distribution, which arises when the proposed scheme is applied to a specific bivariate exponential distribution. Overall, the proposed framework contributes a mathematically grounded, coherent approach to extending classical distributions while preserving interpretability and computational feasibility. Its ability to model uncertainty via bounded noise provides a valuable tool for modern statistical analysis of imperfect or incomplete data.","abstract_html":"We propose a general framework for extending any probability distribution ν to an absolutely continuous distribution with density g(y) =ν(y + A)/|A|, where A is any bounded measurable set of size |A|. This generalized distribution allows the model to adapt to data characteristics that the original (or "base") distribution ν may not fully capture. We show that this generalized distribution corresponds to that of X + U, where X ~ ν and U is uniformly distributed over A, with X and U independent. This convolution-based framework enables the construction of new probability distributions by introducing additive uniform noise to a known parent distribution. Motivated by practical considerations such asimprecise measurements, data contamination, and truncation, the framework offers a flexible and analytically tractable approach to modeling distributional uncertainty. The key idea - representing the observed variable as the sum of a latent signal and bounded noise - produces generalized distributions that preserve the interpretability of the parent model while accommodating real-world imperfections. This dissertation develops the theoretical foundations of the proposed construction, examines its properties, and explores its potential applications. In particular, we apply the framework to construct a new class of Extended Laplace (EL) distributions, designed to model Laplace data affected by independent uniform errors. We derive the fundamental properties of this EL distribution, propose a robust likelihood-based estimation method, and validate its performance through simulation studies. Applications in finance illustrate the EL model's effectiveness in handling real-world data with inherent uncertainties. In the multivariate setting, we also develop a bivariate Bear-Claw distribution, which arises when the proposed scheme is applied to a specific bivariate exponential distribution. Overall, the proposed framework contributes a mathematically grounded, coherent approach to extending classical distributions while preserving interpretability and computational feasibility. Its ability to model uncertainty via bounded noise provides a valuable tool for modern statistical analysis of imperfect or incomplete data.","abstract_has_math":false,"creators":["Saah, David Kofi"],"institution":null,"degree_name":null,"degree_level":"Doctorate Degree","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Kozubowski, Tomasz J"],"committee_chairs":[],"committee_members":["Panorska, Anna K","Sarantsev, Andrey","Hand, Emily","Hand, Adam"],"year":2025,"date_issued":"2025","date_published":"2025","updated_at":"2026-07-27T21:47:47Z","subjects":[],"languages":["en_US","English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarwolf.unr.edu/handle/11714/11553","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Kozubowski, Tomasz J"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Panorska, Anna K","Sarantsev, Andrey","Hand, Emily","Hand, Adam"]},{"key":"dc:creator","label":"Author","values":["Saah, David Kofi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-09-08T18:38:32Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-09-08T18:38:32Z"]},{"key":"dc:date.issued","label":"Date","values":["2025"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctorate Degree"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://scholarwolf.unr.edu/handle/11714/11553"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We propose a general framework for extending any probability distribution ν to an absolutely continuous distribution with density g(y) =ν(y + A)/|A|, where A is any bounded measurable set of size |A|. This generalized distribution allows the model to adapt to data characteristics that the original (or \"base\") distribution ν may not fully capture. We show that this generalized distribution corresponds to that of X + U, where X ~ ν and U is uniformly distributed over A, with X and U independent. This convolution-based framework enables the construction of new probability distributions by introducing additive uniform noise to a known parent distribution. Motivated by practical considerations such asimprecise measurements, data contamination, and truncation, the framework offers a flexible and analytically tractable approach to modeling distributional uncertainty. The key idea - representing the observed variable as the sum of a latent signal and bounded noise - produces generalized distributions that preserve the interpretability of the parent model while accommodating real-world imperfections. This dissertation develops the theoretical foundations of the proposed construction, examines its properties, and explores its potential applications. In particular, we apply the framework to construct a new class of Extended Laplace (EL) distributions, designed to model Laplace data affected by independent uniform errors. We derive the fundamental properties of this EL distribution, propose a robust likelihood-based estimation method, and validate its performance through simulation studies. Applications in finance illustrate the EL model's effectiveness in handling real-world data with inherent uncertainties. In the multivariate setting, we also develop a bivariate Bear-Claw distribution, which arises when the proposed scheme is applied to a specific bivariate exponential distribution. Overall, the proposed framework contributes a mathematically grounded, coherent approach to extending classical distributions while preserving interpretability and computational feasibility. Its ability to model uncertainty via bounded noise provides a valuable tool for modern statistical analysis of imperfect or incomplete data."]},{"key":"dc:format","label":"Dc Format","values":["PDF"]},{"key":"dc:title","label":"Title","values":["Flexible Statistical Models for Imprecise and Uncertain Data: A New Generalization Approach"]}]}],"canonical_facts":{"dc:contributor.advisor":["Kozubowski, Tomasz J"],"dc:contributor.committeemember":["Panorska, Anna K","Sarantsev, Andrey","Hand, Emily","Hand, Adam"],"dc:creator":["Saah, David Kofi"],"dc:date.accessioned":["2025-09-08T18:38:32Z"],"dc:date.available":["2025-09-08T18:38:32Z"],"dc:date.issued":["2025"],"dc:description.abstract":["We propose a general framework for extending any probability distribution ν to an absolutely continuous distribution with density g(y) =ν(y + A)/|A|, where A is any bounded measurable set of size |A|. This generalized distribution allows the model to adapt to data characteristics that the original (or \"base\") distribution ν may not fully capture. We show that this generalized distribution corresponds to that of X + U, where X ~ ν and U is uniformly distributed over A, with X and U independent. This convolution-based framework enables the construction of new probability distributions by introducing additive uniform noise to a known parent distribution. Motivated by practical considerations such asimprecise measurements, data contamination, and truncation, the framework offers a flexible and analytically tractable approach to modeling distributional uncertainty. The key idea - representing the observed variable as the sum of a latent signal and bounded noise - produces generalized distributions that preserve the interpretability of the parent model while accommodating real-world imperfections. This dissertation develops the theoretical foundations of the proposed construction, examines its properties, and explores its potential applications. In particular, we apply the framework to construct a new class of Extended Laplace (EL) distributions, designed to model Laplace data affected by independent uniform errors. We derive the fundamental properties of this EL distribution, propose a robust likelihood-based estimation method, and validate its performance through simulation studies. Applications in finance illustrate the EL model's effectiveness in handling real-world data with inherent uncertainties. In the multivariate setting, we also develop a bivariate Bear-Claw distribution, which arises when the proposed scheme is applied to a specific bivariate exponential distribution. Overall, the proposed framework contributes a mathematically grounded, coherent approach to extending classical distributions while preserving interpretability and computational feasibility. Its ability to model uncertainty via bounded noise provides a valuable tool for modern statistical analysis of imperfect or incomplete data."],"dc:format":["PDF"],"dc:identifier.uri":["https://scholarwolf.unr.edu/handle/11714/11553"],"dc:language":["English"],"dc:language.iso":["en_US"],"dc:title":["Flexible Statistical Models for Imprecise and Uncertain Data: A New Generalization Approach"],"dc:type":["Dissertation"],"thesis:degree_level":["Doctorate Degree"]},"updated_at":"2026-07-27T21:47:47Z"}