Physics:Quantum data analysis/Moments: Difference between revisions
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'''Moments''' summarize the shape of a distribution through quantities such as mean, variance, skewness, kurtosis, or higher weighted averages. In particle-physics analysis, moments can describe multiplicity fluctuations, angular distributions, energy flow, event shapes, and response functions. They condense complex distributions into numbers that can be compared across datasets, models, or event classes.<ref name="cowan">{{cite book |last=Cowan |first=Glen |title=Statistical Data Analysis |publisher=Oxford University Press |year=1998 |isbn=978-0-19-850156-5}}</ref> | |||
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[[File:Quantum_data_analysis_moments_yellow.png|thumb|280px|Moments represented as | [[File:Quantum_data_analysis_moments_yellow.png|thumb|280px|Moments represented as compact summaries of event distributions.]] | ||
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== Statistical meaning == | |||
The first moments describe location and spread, while higher moments probe asymmetry and tails. In finite data samples, moment estimates have statistical uncertainty and can be sensitive to outliers or acceptance edges.<ref name="cowan">{{cite book |last=Cowan |first=Glen |title=Statistical Data Analysis |publisher=Oxford University Press |year=1998 |isbn=978-0-19-850156-5}}</ref> | |||
== Physics use == | |||
Moments are used in fluctuation studies, angular analyses, structure-function measurements, and comparisons of reconstructed and generated distributions. Weighted moments can emphasize particular kinematic regions.<ref name="pdg2024">{{cite journal |collaboration=Particle Data Group |title=Review of Particle Physics |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |year=2024 |doi=10.1103/PhysRevD.110.030001}}</ref> | |||
== Cautions == | |||
A few moments do not uniquely determine a distribution. For interpretation they should be accompanied by bin-by-bin checks, systematic variations, and clear definitions of the event sample and phase space.<ref name="lyons">{{cite book |last=Lyons |first=Louis |title=Statistics for Nuclear and Particle Physicists |publisher=Cambridge University Press |year=1986 |isbn=978-0-521-37934-2}}</ref> | |||
=See also= | =See also= | ||
Revision as of 20:57, 19 May 2026
Moments summarize the shape of a distribution through quantities such as mean, variance, skewness, kurtosis, or higher weighted averages. In particle-physics analysis, moments can describe multiplicity fluctuations, angular distributions, energy flow, event shapes, and response functions. They condense complex distributions into numbers that can be compared across datasets, models, or event classes.[1]
Statistical meaning
The first moments describe location and spread, while higher moments probe asymmetry and tails. In finite data samples, moment estimates have statistical uncertainty and can be sensitive to outliers or acceptance edges.[1]
Physics use
Moments are used in fluctuation studies, angular analyses, structure-function measurements, and comparisons of reconstructed and generated distributions. Weighted moments can emphasize particular kinematic regions.[2]
Cautions
A few moments do not uniquely determine a distribution. For interpretation they should be accompanied by bin-by-bin checks, systematic variations, and clear definitions of the event sample and phase space.[3]
See also
Table of contents (60 articles)
Index
Foundations and experiments
Analysis, measurements and discovery
Full contents
1. Introduction to Particle Physics (5) Back to index
2. Nuts and Bolts (4) Back to index
3. Overview of Particle Collision Experiments (3) Back to index
4. Collision Kinematics and Complex Observables (8) Back to index
5. Basic Measurements (4) Back to index
6. Data Acquisition Electronics and Systems (1) Back to index
7. Event Reconstruction (3) Back to index
8. Monte Carlo Simulations (4) Back to index
9. General Statistical Methods and Data Visualisation (6) Back to index
10. Standard Model Measurements (6) Back to index
11. Searches for New Physics (4) Back to index
12. Data Processing Techniques (4) Back to index
13. Fit Optimisation Techniques (4) Back to index
14. Advanced Data Comprehension Techniques (3) Back to index
15. Machine Learning (1) Back to index
60. Machine Learning
References
- ↑ 1.0 1.1 Cowan, Glen (1998). Statistical Data Analysis. Oxford University Press. ISBN 978-0-19-850156-5.
- ↑ "Review of Particle Physics". Physical Review D 110 (3): 030001. 2024. doi:10.1103/PhysRevD.110.030001.
- ↑ Lyons, Louis (1986). Statistics for Nuclear and Particle Physicists. Cambridge University Press. ISBN 978-0-521-37934-2.
Author: Sergei V. Chekanov
Author: Claude Pruneau
Author: Harold Foppele
Source attribution: Physics:Quantum data analysis/Moments
