Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations

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dc.contributor.authorYılmaz, Abdullah
dc.date.accessioned2025-01-21T16:34:33Z
dc.date.available2025-01-21T16:34:33Z
dc.date.issued2021
dc.departmentKırıkkale Üniversitesi
dc.description.abstractThe inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution. We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper. Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature.
dc.identifier.doi10.31801/cfsuasmas.906339
dc.identifier.endpage887
dc.identifier.issn1303-5991
dc.identifier.issue2
dc.identifier.startpage871
dc.identifier.trdizinid499014
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.906339
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay499014
dc.identifier.urihttps://hdl.handle.net/20.500.12587/23985
dc.identifier.volume70
dc.identifier.wosWOS:000851379300020
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakTR-Dizin
dc.language.isoen
dc.publisherAnkara Univ, Fac Sci
dc.relation.ispartofCommunications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241229
dc.subjectCircular distribution; inverse stereographic; bilinear transformation; Mobius transformation; rotation
dc.titleInverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations
dc.typeArticle

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