Information-Loss Location Estimation and Curvature-Scale Analysis of Physical Measurements: A Gaussian, Cauchy, and Logistic Neutron-Lifetime Benchmark
Abstract
We develop and implement a two-step location-scale analysis for repeated physical measurements when the underlying distribution is not known. For a chosen substitute distribution, stationarity of population Kullback-Leibler information loss at fixed scale motivates the location score, which we apply to the observed measurements through empirical cross-entropy. Steiner's curvature rule then defines a companion scale separately. We place Gaussian, Cauchy, and logistic substitutes in one common construction and implement them reproducibly on a physics benchmark. For the logistic substitute, we pair the established bounded location score with a scale defined by the curvature rule rather than by a fitted tuning constant or a scale-likelihood equation. For Gaussian measurements with different quoted uncertainties, an experiment-level curvature convention and a stated variance mapping give an exact algebraic connection to a standard residual-based variance estimate for a weighted fit. Applied to a published 21-measurement neutron-lifetime compilation, the inverse-variance weighted, most frequent value, and logistic locations are 878.689, 881.164, and 882.835 s, respectively. These values are benchmark results of the compared constructions and are not proposed as a new recommended neutron lifetime.
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BibTeX
@misc{golovko2026informationloss,
title = {{Information-Loss Location Estimation and Curvature-Scale Analysis of Physical Measurements: A Gaussian, Cauchy, and Logistic Neutron-Lifetime Benchmark}},
author = {Victor V. Golovko},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14793},
eprint = {2609.14793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14793},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Information-Loss Location Estimation and Curvature-Scale Analysis of Physical Measurements: A Gaussian, Cauchy, and Logistic Neutron-Lifetime Benchmark
AU - Victor V. Golovko
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14793
UR - https://arxiv.org/abs/2609.14793
AB - We develop and implement a two-step location-scale analysis for repeated physical measurements when the underlying distribution is not known. For a chosen substitute distribution, stationarity of population Kullback-Leibler information loss at fixed scale motivates the location score, which we apply to the observed measurements through empirical cross-entropy. Steiner's curvature rule then defines a companion scale separately. We place Gaussian, Cauchy, and logistic substitutes in one common construction and implement them reproducibly on a physics benchmark. For the logistic substitute, we pair the established bounded location score with a scale defined by the curvature rule rather than by a fitted tuning constant or a scale-likelihood equation. For Gaussian measurements with different quoted uncertainties, an experiment-level curvature convention and a stated variance mapping give an exact algebraic connection to a standard residual-based variance estimate for a weighted fit. Applied to a published 21-measurement neutron-lifetime compilation, the inverse-variance weighted, most frequent value, and logistic locations are 878.689, 881.164, and 882.835 s, respectively. These values are benchmark results of the compared constructions and are not proposed as a new recommended neutron lifetime.
ER -