Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones

Guillermo Martínez-Flórez, Roger Tovar-Falón, Víctor Leiva () and Cecilia Castro ()
Additional contact information
Guillermo Martínez-Flórez: Department of Mathematics and Statistics, Universidad de Córdoba, Montería 230002, Colombia
Roger Tovar-Falón: Department of Mathematics and Statistics, Universidad de Córdoba, Montería 230002, Colombia
Víctor Leiva: School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
Cecilia Castro: Centre of Mathematics, Universidade do Minho, 4710-057 Braga, Portugal

Mathematics, 2024, vol. 12, issue 16, 1-23

Abstract: The modeling of data involving proportions, confined to a unit interval, is crucial in diverse research fields. Such data, expressing part-to-whole relationships, span from the proportion of individuals affected by diseases to the allocation of resources in economic sectors and the survival rates of species in ecology. However, modeling these data and interpreting information obtained from them present challenges, particularly when there is high zero–one inflation at the extremes of the unit interval, which indicates the complete absence or full occurrence of a characteristic or event. This inflation limits traditional statistical models, which often fail to capture the underlying distribution, leading to biased or imprecise statistical inferences. To address these challenges, we propose and derive the skew-normal zero–one inflated (SNZOI) models, a novel class of asymmetric regression models specifically designed to accommodate zero–one inflation presented in the data. By integrating a continuous-discrete mixture distribution with covariates in both continuous and discrete parts, SNZOI models exhibit superior capability compared to traditional models when describing these complex data structures. The applicability and effectiveness of the proposed models are demonstrated through case studies, including the analysis of medical data. Precise modeling of inflated proportion data unveils insights representing advancements in the statistical analysis of such studies. The present investigation highlights the limitations of existing models and shows the potential of SNZOI models to provide more accurate and precise inferences in the presence of zero–one inflation.

Keywords: censoring; proportion data; regression; skew-normal model; truncation; zero–one inflation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/16/2486/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/16/2486/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:16:p:2486-:d:1454749

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().