Fourier Transform by Distribution Function in Statistics

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dc.contributor.authorYalaz, Seçil
dc.date.accessioned2025-02-22T14:13:30Z
dc.date.available2025-02-22T14:13:30Z
dc.date.issued2024
dc.departmentDicle Üniversitesien_US
dc.description.abstractThe Fourier transform is one of the most important methods, which has the ability to transform complex integral equations into simple algebraic equations and is frequently used in both mathematics and statistics. Although the Fourier transform is valid for every function in mathematics under certain conditions, this situation can become more complicated in statistics because of the fact that statistics are very different from mathematics. While in statistics, different observation values, that is, different x values, are considered for each situation, in mathematics for each x a function is defined. Because in statistics, random variables are concerned rather than functions, and the density functions of the observed values of interest should also be known. In statistics, it is seen that the Fourier transform is used in non-parametric models in which asymptotic properties are examined. In the Fourier transform, which can be performed using both distribution and density functions, it is not possible to use the density function when there are unknown or non-integrable density functions or very slow convergence rate (considering asymptotic properties). In such cases, it would be more appropriate to perform the Fourier transform with the distribution function. In this study, suggestions are presented on under which conditions it would be more appropriate to perform the Fourier transform with the distribution function.en_US
dc.identifier.doi10.47495/okufbed.1242108
dc.identifier.endpage591en_US
dc.identifier.issn2687-3729
dc.identifier.issue2en_US
dc.identifier.startpage581en_US
dc.identifier.trdizinid1227634en_US
dc.identifier.urihttps://doi.org/10.47495/okufbed.1242108
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/1227634
dc.identifier.urihttps://hdl.handle.net/11468/30020
dc.identifier.volume7en_US
dc.indekslendigikaynakTR-Dizin
dc.institutionauthorYalaz, Seçil
dc.language.isoenen_US
dc.relation.ispartofOsmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi (Online)en_US
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmzKA_TR_20250222
dc.subjectFourier dönüşümüen_US
dc.subjectDağılım fonksiyonuen_US
dc.subjectAsimptotik özellikleren_US
dc.subjectİntegrallenebilmeen_US
dc.subjectÖlçüm hatalı değişkenleren_US
dc.subjectYoğunluk fonksiyonuen_US
dc.titleFourier Transform by Distribution Function in Statisticsen_US
dc.typeArticleen_US

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