Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00209 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911474475073536 |
|---|---|
| author | Turan, Meltem Munkhammar, Joakim |
| author_facet | Turan, Meltem Munkhammar, Joakim |
| contents | Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and sensitivity to the choice of support. This work proposes a quantile-based piecewise polynomial density reconstruction approach that combines equal-probability binning with local moment-matched polynomials within each bin. Two variants are considered: piecewise monomial and piecewise Lagrange polynomials with Chebyshev nodes. The numbers of bins and polynomial degrees are selected by a proposed grid search approach guided by the Kolmogorov-Smirnov (K-S) test statistic under non-negativity constraints. Across several benchmark distributions, the proposed methods reduce K-S errors by about $80$-$96\%$ relative to standard monomial and Lagrange polynomial approaches, and by about $83$-$97\%$ compared with spline density estimation. For real-world household electricity consumption and solar irradiance data, the piecewise approaches achieve K-S test statistic performance comparable to kernel density estimation while offering improved control over tail behavior and oscillations. Overall, the results demonstrate that quantile-based localization substantially enhances the robustness and fidelity of moment-based polynomial PDF reconstruction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moment-based Piecewise Polynomial Probability Density Estimation with Quantile-Based Binning Turan, Meltem Munkhammar, Joakim General Mathematics 62E17 Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and sensitivity to the choice of support. This work proposes a quantile-based piecewise polynomial density reconstruction approach that combines equal-probability binning with local moment-matched polynomials within each bin. Two variants are considered: piecewise monomial and piecewise Lagrange polynomials with Chebyshev nodes. The numbers of bins and polynomial degrees are selected by a proposed grid search approach guided by the Kolmogorov-Smirnov (K-S) test statistic under non-negativity constraints. Across several benchmark distributions, the proposed methods reduce K-S errors by about $80$-$96\%$ relative to standard monomial and Lagrange polynomial approaches, and by about $83$-$97\%$ compared with spline density estimation. For real-world household electricity consumption and solar irradiance data, the piecewise approaches achieve K-S test statistic performance comparable to kernel density estimation while offering improved control over tail behavior and oscillations. Overall, the results demonstrate that quantile-based localization substantially enhances the robustness and fidelity of moment-based polynomial PDF reconstruction. |
| title | Moment-based Piecewise Polynomial Probability Density Estimation with Quantile-Based Binning |
| topic | General Mathematics 62E17 |
| url | https://arxiv.org/abs/2603.00209 |