Academic Journal
On the effect of fixed-bandwidth kernel density estimation on the exponential distribution.
| Τίτλος: | On the effect of fixed-bandwidth kernel density estimation on the exponential distribution. |
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| Συγγραφείς: | Bataihah, Anwar |
| Πηγή: | Journal of Nigerian Society of Physical Sciences; Aug2026, Vol. 8 Issue 3, p1-10, 10p |
| Θεματικοί όροι: | Statistical smoothing, Nonparametric statistics, Eigenfunctions, Probability density function, Distribution (Probability theory) |
| Περίληψη: | Kernel density estimation (KDE) is widely used as a nonparametric smoothing operator in statistics. In this work, we study fixed-bandwidth KDE as a convolution operator applied to an exponential baseline distribution with rate parameter β > 0. We show that, for any compactly supported kernel K on [-1, 1] and any fixed bandwidth h > 0, the expected KDE admits an exact factorization in the interior region y ≥ h: E[bf (y)] = βe-βyC0, where C0 = R 1 -1 K(u)eβhu du depends only on the kernel and bandwidth. Thus, the exponential density is an eigenfunction of the kernel-smoothing operator in the interior domain: its shape is preserved up to multiplication by the eigenvalue C0. After normalization on [h,∞), the resulting distribution reduces exactly to the shifted exponential density βe-β(y-h). The result clarifies the role of boundary effects in kernel smoothing and shows that fixed-bandwidth KDE does not generate new parametric families from exponential baselines under tail normalization. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Nigerian Society of Physical Sciences is the property of Nigerian Society of Physical Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Biomedical Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edm DbLabel: Biomedical Index An: 196781224 RelevancyScore: 1082 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1082.42456054688 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the effect of fixed-bandwidth kernel density estimation on the exponential distribution. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bataihah%2C+Anwar%22">Bataihah, Anwar</searchLink> – Name: TitleSource Label: Source Group: Src Data: Journal of Nigerian Society of Physical Sciences; Aug2026, Vol. 8 Issue 3, p1-10, 10p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Statistical+smoothing%22">Statistical smoothing</searchLink><br /><searchLink fieldCode="DE" term="%22Nonparametric+statistics%22">Nonparametric statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+density+function%22">Probability density function</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Kernel density estimation (KDE) is widely used as a nonparametric smoothing operator in statistics. In this work, we study fixed-bandwidth KDE as a convolution operator applied to an exponential baseline distribution with rate parameter β > 0. We show that, for any compactly supported kernel K on [-1, 1] and any fixed bandwidth h > 0, the expected KDE admits an exact factorization in the interior region y ≥ h: E[bf (y)] = βe-βyC0, where C0 = R 1 -1 K(u)eβhu du depends only on the kernel and bandwidth. Thus, the exponential density is an eigenfunction of the kernel-smoothing operator in the interior domain: its shape is preserved up to multiplication by the eigenvalue C0. After normalization on [h,∞), the resulting distribution reduces exactly to the shifted exponential density βe-β(y-h). The result clarifies the role of boundary effects in kernel smoothing and shows that fixed-bandwidth KDE does not generate new parametric families from exponential baselines under tail normalization. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Journal of Nigerian Society of Physical Sciences is the property of Nigerian Society of Physical Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.46481/jnsps.2026.3590 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 1 Subjects: – SubjectFull: Statistical smoothing Type: general – SubjectFull: Nonparametric statistics Type: general – SubjectFull: Eigenfunctions Type: general – SubjectFull: Probability density function Type: general – SubjectFull: Distribution (Probability theory) Type: general Titles: – TitleFull: On the effect of fixed-bandwidth kernel density estimation on the exponential distribution. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bataihah, Anwar IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 27142817 Numbering: – Type: volume Value: 8 – Type: issue Value: 3 Titles: – TitleFull: Journal of Nigerian Society of Physical Sciences Type: main |
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