The unit folded normal distribution: a new unit probability distribution with the estimation procedures, quantile regression modeling and educational attainment applications

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dc.authorid0000-0003-3302-0705en_US
dc.authorid0000-0002-3466-8119en_US
dc.contributor.authorKorkmaz, Mustafa Çağatay
dc.contributor.authorChesneau, Christophe
dc.contributor.authorKorkmaz, Zehra Sedef
dc.date.accessioned2022-06-16T10:35:37Z
dc.date.available2022-06-16T10:35:37Z
dc.date.issued2022
dc.departmentAÇÜ, Eğitim Fakültesi, Eğitim Bilimleri Bölümüen_US
dc.description.abstractIn this paper, we develop a continuous distribution on the unit interval characterized by the distribution of the absolute hyperbolic tangent transformation of a random variable following the normal distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions on the unit interval is a motivation for the study. First, we study it theoretically and discuss its properties of interest from a modeling point of view. In particular, it is shown that the proposed distribution accommodates various levels of skewness and kurtosis. Then, some statistical work is performed. We investigate diverse estimation methods for the involved parameters and evaluate their performance through two simulation studies. Subsequently, the quantile regression model derived from the proposed distribution is developed. Two real-world data applications of interest are provided. The first application is about the univariate modeling of the percentage of the educational attainment of some countries, which is one indicator of the education topic of the Better Life Index (BLI) of the Organization for Economic Co-operation and Development (OECD) countries. The second application is to explain the relationship between the percentage of educational attainment of some countries with one indicator of the work-life balance, safety, and health topics of BLI via median quantile regression modeling. For the considered data sets, the proposed distribution and quantile regression models show that they have better modeling abilities than competitive models under some comparison criteria. The results also indicate that covariates are (statistically) significant at any ordinary level of significance for the median response.
dc.identifier.citationKorkmaz, M. Ç., Chesneau, C., & Korkmaz, Z. S. (2022). The Unit Folded Normal Distribution: A New Unit Probability Distribution with the Estimation Procedures, Quantile Regression Modeling and Educational Attainment Applications. Journal of Reliability and Statistical Studies, 15(1), 261-298.en_US
dc.identifier.doi10.13052/jrss0974-8024.15111
dc.identifier.endpage298en_US
dc.identifier.issue1en_US
dc.identifier.scopusqualityQ3
dc.identifier.startpage261en_US
dc.identifier.urihttps://hdl.handle.net/11494/3859
dc.identifier.volume15en_US
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorKorkmaz, Mustafa Çağatay
dc.institutionauthorKorkmaz, Zehra Sedef
dc.language.isoenen_US
dc.publisherRiver Publishersen_US
dc.relation.ispartofJournal of Reliability and Statistical Studies
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectBetter life indexen_US
dc.subjectEducational attainmenten_US
dc.subjectNormal distributionen_US
dc.subjectPoint estimatesen_US
dc.subjectOECD data setsen_US
dc.subjectQuantile regressionen_US
dc.subjectUnit distributionen_US
dc.titleThe unit folded normal distribution: a new unit probability distribution with the estimation procedures, quantile regression modeling and educational attainment applicationsen_US
dc.typeArticle

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