CoChat
Sign Up
Cited by 2,621Statistical Distribution Estimation and ApplicationsProbability and Statistical ResearchStatistical Methods and Applications

The DOI matches its Crossref record; 56 of the 57 references it cites were found in a registry or an index.

Log-normal Distributions across the Sciences: Keys and Clues

LIMPERT, ECKHARD, STAHEL, WERNER A., ABBT, MARKUS·2001·BioScience
DOI 10.1641/0006-3568(2001)051[0341:lndats]2.0.co;2
Open this paper in CoChat — free account

Abstract

As the need grows for conceptualization, formalization, and abstraction in biology, so too does mathematics' relevance to the field (Fagerström et al. 1996). Mathematics is particularly important for analyzing and characterizing random variation of, for example, size and weight of individuals in populations, their sensitivity to chemicals, and time-to-event cases, such as the amount of time an individual needs to recover from illness. The frequency distribution of such data is a major factor determining the type of statistical analysis that can be validly carried out on any data set. Many widely used statistical methods, such as ANOVA (analysis of variance) and regression analysis, require that the data be normally distributed, but only rarely is the frequency distribution of data tested when these techniques are used. The Gaussian (normal) distribution is most often assumed to describe the random variation that occurs in the data from many scientific disciplines; the well-known bell-shaped curve can easily be characterized and described by two values: the arithmetic mean x and the standard deviation s, so that data sets are commonly described by the expression x ± s. A historical example of a normal distribution is that of chest measurements of Scottish soldiers made by Quetelet, Belgian founder of modern social statistics (Swoboda 1974). In addition, such disparate phenomena as milk production by cows and random deviations from target values in industrial processes fit a normal distribution.

Overview

Integrity signals

Registry

Crossref · 10.1641/0006-3568(2001)051[0341:lndats]2.0.co;2

Cites

56 of 56 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Interaction times were initially conditionally lognormal.

    “Interaction times were initially conditionally lognormal, a common occurrence with temporal measures [50].”

    From Understanding and Improving Drilled-Down Information Extraction from Online Data Visualizations for Screen-Reader Users (2023) · cites this paper as [50]

  • The receptor affinity distribution (RAD) inferred via string matching is broadly applicable to the immune and olfactory systems and portrays a Poisson distribution, approximated by a lognormal distribution in GARD applications.

    “Along these lines, we have inferred a receptor affinity distribution (RAD) broadly applicable to the immune and olfactory systems via a close analogue of string matching [65,79]. This portrayed a Poisson distribution, which in GARD applications [54] was approximated by a lognormal distribution [80].”

    From Systems protobiology: origin of life in lipid catalytic networks (2018) · cites this paper as [80]

  • The visual nature of data visualizations inherently disenfranchises screen-reader users, who may not be able to see or recognize visual patterns.

    “However, the visual nature of data visualizations inherently disenfranchises screen-reader users, who may not be able to see or recognize visual patterns [52,57].”

    From VoxLens: Making Online Data Visualizations Accessible with an Interactive JavaScript Plug-In (2022) · cites this paper as [52]

  • Many biological systems exhibit log-normally distributed errors arising from multiplicative errors.

    “Note that many biological systems exhibit log-normally distributed errors arising from multiplicative errors [49,92].”

    From Parameter uncertainty in biochemical models described by ordinary differential equations (2013) · cites this paper as [92]

Citations

Cites

Flagged first, then by citations

1 of the 57 references couldn’t be matched to a known paper.

Research works printed but not linked: 3

  1. Kondo, 1977, Japanese Journal of Human Genetics, 21, 217
  2. Razumovsky, 1940, Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS, 9, 814
  3. Williams, 1940, Biometrika, 31, 356

Cited by

Sorted by citations

Related

Metadata

Authors
LIMPERT, E., STAHEL, W. A., & ABBT, M.
Affiliations
ETH Zurich (CH)
Corresponding author
LIMPERT, ECKHARD
ORCID
STAHEL, WERNER A.
Venue
BioScience
Publisher
Oxford University Press (OUP)
Published
2001
Volume
51
Issue
5
Pages
341
ISSN
0006-3568 (ISSN-L)
DOI
10.1641/0006-3568(2001)051[0341:lndats]2.0.co;2
OpenAlex
W2264709743
Cited by
2,621
References
57
Citations by year
2026: 141 · 2025: 107 · 2024: 99 · 2023: 79 · 2022: 115 · 2021: 143 · 2020: 125 · 2019: 176 · 2018: 132 · 2017: 147 · 2016: 156 · 2015: 126 · 2014: 144 · 2013: 142 · 2012: 150
FWCI
19.85
Type
journal article
Language
en
Open access
closed
Locations
  • BioScience (publishedVersion)
  • BioOne Complete (BioOne) (submittedVersion)
Funders
University of Reading
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 › Statistical Methods and Applications
Keywords
lognormal distribution, normal distribution, frequency distribution, random variation, biological variation, normality assumption, analysis of variance, regression analysis, bell-shaped curve

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 ›

Are you an author, or do you see a problem with this page? Request a review