Kurtosis as Peakedness, 1905–2014. R.I.P.
Open accessAbstract
The incorrect notion that kurtosis somehow measures "peakedness" (flatness, pointiness or modality) of a distribution is remarkably persistent, despite attempts by statisticians to set the record straight. This article puts the notion to rest once and for all. Kurtosis tells you virtually nothing about the shape of the peak - its only unambiguous interpretation is in terms of tail extremity; i.e., either existing outliers (for the sample kurtosis) or propensity to produce outliers (for the kurtosis of a probability distribution). To clarify this point, relevant literature is reviewed, counterexample distributions are given, and it is shown that the proportion of the kurtosis that is determined by the central μ ± σ range is usually quite small.
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Kurtosis feature can provide information regarding the non-Gaussianity or impulsiveness of the vibration signals.
“Kurtosis feature can provide the information regarding the non-Gaussianity or impulsiveness of the vibration signals [68,69].”
From Vibration Analysis for Machine Monitoring and Diagnosis: A Systematic Review (2021) · cites this paper as [68]
Section 3 (“How Data Look”; page unavailable) says sample kurtosis primarily reflects outliers, supporting its use as an indicator of extreme or impulsive observations. Section 4 compares kurtosis with that of a normal distribution, but the paper does not examine vibration signals or establish kurtosis as a measure of their non-Gaussianity. (LLM, conf=0.84)
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- Authors
- Westfall, P. H.
- Affiliations
- Texas Tech University (US)
- Corresponding author
- Westfall, Peter H.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 2014-07-03
- Volume
- 68
- Issue
- 3
- Pages
- 191-195
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- PMC
- PMC4321753
- OpenAlex
- W1966994480
- Cited by
- 518
- References
- 32
- Citations by year
- 2026: 34 · 2025: 57 · 2024: 35 · 2023: 46 · 2022: 59 · 2021: 73 · 2020: 70 · 2019: 69 · 2018: 39 · 2017: 22 · 2016: 10 · 2015: 2 · 2014: 2
- FWCI
- 12.69
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- The American Statistician (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Institutes of Health
- National Institute of Diabetes and Digestive and Kidney Diseases (R01DK089167)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- kurtosis, peakedness, outliers, distribution shape, sample kurtosis, probability distributions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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