Physics:Quantum data analysis/Moments
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
Full contents
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.
Source attribution: Physics:Quantum data analysis/Moments
