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Low Moments for Small Samples: A Comparative Study of Order Statistics
Open accessAbstract
The means, variances, and covariances for samples of size $\leq 10$ from the normal distribution, a selected long-tailed distribution, and the uniform distribution are tabled and compared with the usual asymptotic approximations. The methods of computation used and the accuracy expected are discussed. Use is made of the representation of an arbitrarily distributed variate as a monotone function of a uniformly (rectangularly) distributed variate. It is hoped that these tables will encourage experimentation with new statistical procedures.
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“For example, outliers in linear models may strongly impact linear estimators, and some studies may therefore adopt a modeling strategy wherein values are winsorized (e.g., extreme values can be truncated at the 2.5th and 97.5th quantiles56).”
From Guidelines for wrist-worn consumer wearable assessment of heart rate in biobehavioral research (2020) · cites this paper as [56]
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An analysis of variance test for normality (complete samples)
SHAPIRO, S. S., & WILK, M. B. (1965) · Biometrika · doi:10.1093/biomet/52.3-4.591 · Cited by 23,480
A Comparative Study of Various Tests for Normality
Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968) · Journal of the American Statistical Association · doi:10.1080/01621459.1968.10480932 · Cited by 1,192
Metabolic Reconstruction for Metagenomic Data and Its Application to the Human Microbiome
Abubucker, S., Segata, N., Goll, J. B., Schubert, A. M., Izard, J., Cantarel, B. L., Rodriguez-Mueller, B., Zucker, J., Thiagarajan, M., Henrissat, B., et al. (2012) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002358 · Cited by 1,076
“These differences were summarized into overall patterns of variation using principal component analysis on a matrix of average module abundances per body site, Winsorized at 20% (a robust arithmetic mean [30]), filtered at a minimum of 0.01% in at least one site, and normalized to z-scores.”
MethodInfluentialComparisons of various types of normality tests
Yap, B. W., & Sim, C. H. (2011) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2010.520163 · Cited by 897
“gif"/> , originally proposed by Ramberg and Schmeiser 36 , is a four-parameter generalization of the two-parameter Tukey's Lambda family of distribution 37 and Karian and Dudewicz 38 has published tables that provide parameter <inline-graphic xmlns:xlink="http://www.”
BackgroundGenome-wide probing of RNA structure reveals active unfolding of mRNA structures in vivo
Rouskin, S., Zubradt, M., Stefan Washietl, A., Kellis, M., & Weissman, J. S. (2013) · Nature · doi:10.1038/nature12894 · Cited by 862
Metadata
- Authors
- Hastings, C., Mosteller, F., Tukey, J. W., & Winsor, C. P.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1947-09
- Volume
- 18
- Issue
- 3
- Pages
- 413-426
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W2040509998
- Cited by
- 366
- References
- 0
- Citations by year
- 2026: 18 · 2025: 10 · 2024: 10 · 2023: 14 · 2022: 18 · 2021: 27 · 2020: 24 · 2019: 22 · 2018: 18 · 2017: 26 · 2016: 17 · 2015: 17 · 2014: 14 · 2013: 14 · 2012: 14
- FWCI
- 6.85
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Annals of Mathematical Statistics (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- order statistics, moments, normal distribution, long-tailed distributions, uniform distribution, asymptotic approximation, mathematical tables
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