Precision of Gaussian, Lorentzian, and pseudo-Voigt peak fitting under Gaussian noise
- 1Research Institute for Marine Geodynamics
- 2Japan Agency for Marine-Earth Science and Technology
Abstract
Discriminating subtle differences in measured signals is essential to scientific discovery. Knowledge of the attainable precision limits of fitted peak parameters and the physical and statistical factors that determine them provides a rational basis for improving this capability. However, without a common framework for comparing peak shapes and noise statistics, universal features of peak-parameter precision remain difficult to distinguish from those specific to a profile or noise regime, thereby hindering the development of general guidance for peak fitting and measurement design. Here we analyze Gaussian, Lorentzian, and pseudo-Voigt profiles in the Gaussian-noise (GN) limit using the same information-theoretic parameterization established for the Poisson-noise (PN) limit, enabling direct comparisons across peak shapes and noise regimes. Using the Fisher information matrix and the Cramér–Rao inequality, we derive analytical lower bounds on the standard deviations of peak intensity (I), center (ωc), full width at half maximum (Γ), area (A), and mixing parameter (η) and validate them against numerical calculations and Monte Carlo simulations. This unified framework addresses a long-standing question in peak analysis: whether intensity ratios or area ratios can be estimated more precisely. Whereas PN-limit theory predicts greater precision for area ratios across all three profiles, our GN-limit analysis shows that this advantage disappears for Gaussian and Lorentzian profiles and reverses for a pseudo-Voigt model with free η. Thus, neither I- nor A-based quantification is intrinsically more precise; their relative precision is governed by peak shape, parameter covariance, and noise statistics. This helps explain why experimental comparisons have not yielded a unique answer and provides a principled basis for selecting the more precise quantity. Fisher-information densities further show that information on I is concentrated in the peak core, information on ωc is concentrated on the flanks, and information on Γ and η extends into the wings. This indicates that precise estimation of Γ and η requires the fitting range to extend sufficiently into the peak wings. Finally, using Raman spectroscopy as an example, we combine the theory with detector-noise models to predict attainable precision before data acquisition and quantify how measurement conditions and instrument performance affect precision. The framework supports quantitative optimization of measurement conditions and instrument design to improve analytical precision across diverse signal-analysis applications.
Related
- Alternative Equations and 'Pseudo-statistical' Approaches that Enhance the Precision of Initial Rates for the Determination of Kinetic Parameters
- High-Throughput Voigt Deconvolution of Luminescence Spectral Maps with Curvature-Informed Peak Initialization
- SFEModeling.jl: multi-model, multi-curve fitting of supercritical fluid extraction kinetics with a graphical interface
- Uncertainty-Driven Self-Refinement of Adaptive Kolmogorov-Arnold Networks for Fitting Nonadiabatic Potential Energy Surface
- Fitting of unary isotherms in MOFs and zeolites: Are saturation capacities and Freundlich exponents temperature-dependent?
BibTeX
@misc{hagiwara2026precision,
title = {{Precision of Gaussian, Lorentzian, and pseudo-Voigt peak fitting under Gaussian noise}},
author = {Yuuki Hagiwara and Tatsu Kuwatani},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009613/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009613/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Precision of Gaussian, Lorentzian, and pseudo-Voigt peak fitting under Gaussian noise
AU - Yuuki Hagiwara
AU - Tatsu Kuwatani
PY - 2026
DA - 2026/09/29
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009613/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009613/v1
AB - Discriminating subtle differences in measured signals is essential to scientific discovery. Knowledge of the attainable precision limits of fitted peak parameters and the physical and statistical factors that determine them provides a rational basis for improving this capability. However, without a common framework for comparing peak shapes and noise statistics, universal features of peak-parameter precision remain difficult to distinguish from those specific to a profile or noise regime, thereby hindering the development of general guidance for peak fitting and measurement design. Here we analyze Gaussian, Lorentzian, and pseudo-Voigt profiles in the Gaussian-noise (GN) limit using the same information-theoretic parameterization established for the Poisson-noise (PN) limit, enabling direct comparisons across peak shapes and noise regimes. Using the Fisher information matrix and the Cramér–Rao inequality, we derive analytical lower bounds on the standard deviations of peak intensity (I), center (ωc), full width at half maximum (Γ), area (A), and mixing parameter (η) and validate them against numerical calculations and Monte Carlo simulations. This unified framework addresses a long-standing question in peak analysis: whether intensity ratios or area ratios can be estimated more precisely. Whereas PN-limit theory predicts greater precision for area ratios across all three profiles, our GN-limit analysis shows that this advantage disappears for Gaussian and Lorentzian profiles and reverses for a pseudo-Voigt model with free η. Thus, neither I- nor A-based quantification is intrinsically more precise; their relative precision is governed by peak shape, parameter covariance, and noise statistics. This helps explain why experimental comparisons have not yielded a unique answer and provides a principled basis for selecting the more precise quantity. Fisher-information densities further show that information on I is concentrated in the peak core, information on ωc is concentrated on the flanks, and information on Γ and η extends into the wings. This indicates that precise estimation of Γ and η requires the fitting range to extend sufficiently into the peak wings. Finally, using Raman spectroscopy as an example, we combine the theory with detector-noise models to predict attainable precision before data acquisition and quantify how measurement conditions and instrument performance affect precision. The framework supports quantitative optimization of measurement conditions and instrument design to improve analytical precision across diverse signal-analysis applications.
ER -