Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
On the effect of fixed-bandwidth kernel density estimation on the exponential distribution. |
| 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] |
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| Βάση Δεδομένων: |
Biomedical Index |