#normal-distribution — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #normal-distribution, aggregated by home.social.
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“It’s the bell curve again”*…
Joseph Howlett on how the central limit theorem, which started as a bar trick for 18th-century gamblers, became something on which scientists rely every day…
No matter where you look, a bell curve is close by.
Place a measuring cup in your backyard every time it rains and note the height of the water when it stops: Your data will conform to a bell curve. Record 100 people’s guesses at the number of jelly beans in a jar, and they’ll follow a bell curve. Measure enough women’s heights, men’s weights, SAT scores, marathon times — you’ll always get the same smooth, rounded hump that tapers at the edges.
Why does the bell curve pop up in so many datasets?
The answer boils down to the central limit theorem, a mathematical truth so powerful that it often strikes newcomers as impossible, like a magic trick of nature. “The central limit theorem is pretty amazing because it is so unintuitive and surprising,” said Daniela Witten, a biostatistician at the University of Washington. Through it, the most random, unimaginable chaos can lead to striking predictability.
It’s now a pillar on which much of modern empirical science rests. Almost every time a scientist uses measurements to infer something about the world, the central limit theorem is buried somewhere in the methods. Without it, it would be hard for science to say anything, with any confidence, about anything.
“I don’t think the field of statistics would exist without the central limit theorem,” said Larry Wasserman, a statistician at Carnegie Mellon University. “It’s everything.”
Perhaps it shouldn’t come as a surprise that the push to find regularity in randomness came from the study of gambling…
Read on for the fascinating story of: “The Math That Explains Why Bell Curves Are Everywhere,” from @quantamagazine.bsky.social.
Howlett concludes by observing that “The central limit theorem is a pillar of modern science, ultimately, because it’s a pillar of the world around us. When we combine lots of independent measurements, we get clusters. And if we’re clever enough, we can use those clusters to find out something interesting about the processes that made them”– which follows from the story he shares.
Still, we’d do well to remember that there are limits to its applicability, both descriptively (as Nassim Nicholas Taleb points out, “because the bell curve ignores large deviations, cannot handle them, yet makes us confident that we have tamed uncertainty”) and prescriptively (as Benjamim Bloom argues, “The bell-shaped curve is not sacred. It describes the outcome of a random process. Since education is a purposeful activity….the achievement distribution should be very different from the normal curve if our instruction is effective).
For (much) more, see Peter Bernstein‘s wonderful Against the Gods: The Remarkable Story of Risk
* Robert A. Heinlein, Time Enough for Love
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As we noodle on the normal distribution, we might send curve-shattering birthday greetings to Norman Borlaug; he was born on ths date in 1914. An agronomist, he developed and led initiatives worldwide that contributed to the voluminous increases in agricultural production we call “the Green Revolution.” Borlaug was awarded multiple honors for his work, including the Nobel Peace Prize, the Presidential Medal of Freedom, and the Congressional Gold Medal; he’s one of only seven people to have received all three of those awards.
#agriculture #BellCurve #centralLimitTheorem #culture #GreenRevolution #history #Mathematics #normalDistribution #NormanBorlaug #Science #statistics -
‘Tech oligarchs reshape humanity while billionaires of old seem quaint’
https://www.theguardian.com/technology/2026/mar/08/billionaires-tech-oligarchs
Those financing a genocidal and ecocidal war on the democratic rights of diverse interests are so far from being quaint, that they have normalised the absurd! The many though can tell the difference between an abnormal, with extreme inequalities and injustices, and the normal, and sustainable distribution of rights freedom! #FascistWarsAlwaysFail #TheGreatCollapseOfEmpire #AbnormalDistribution #MadEmperor #DeathAndEcocide #NormalDistribution #Freedom #BuildingTheFederation
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"A generalized linear model or #GLM consists of three components:
1. A random component, specifying the conditional distribution of the response variable, Yᵢ (for the ith of n independently sampled observations). […]
2. A linear predictor—that is a linear function of regressors,
ηᵢ = α + Σⱼ Xᵢⱼ*βⱼ
3. A smooth and invertible link function g(·), which transforms the expectation of the response variable, μᵢ ≡ E(Yᵢ), to the linear predictor:
g(μᵢ) = ηᵢ"https://www.sagepub.com/sites/default/files/upm-binaries/21121_Chapter_15.pdf
#models #dataDev #logNormal #regression #normality #normalDistribution #gamma #Γ #modelling #modeling #AIDev #ML #evaluation
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How to assess a statistical model?
How to choose between variables?Pearson's #correlation is irrelevant if you suspect that the relationship is not a straight line.
If monotonic relationship:
"#Spearman’s rho is particularly useful for small samples where weak correlations are expected, as it can detect subtle monotonic trends." It is "widespread across disciplines where the measurement precision is not guaranteed".
"#Kendall’s Tau-b is less affected [than Spearman’s rho] by outliers in the data, making it a robust option for datasets with extreme values."
Ref: https://statisticseasily.com/kendall-tau-b-vs-spearman/#normality #normalDistribution #modeling #dataDev #AIDev #ML #modelEvaluation #regression #modelling #dataLearning #featureEngineering #linearRegression #modeling #probability #probabilities #statistics #stats #correctionRatio #ML #Pearson #bias #regressionRedress #distributions
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"The #gamma GLM is a relatively assumption-light means of #modeling non-negative data, given gamma's flexibility.
[…]
"Explaining what is used and what is not used, despite merits and demerits […]: Loosely, the larger the internal literature in any field on modelling techniques, the less inclined people in that field seem to be to try something different."Nick Cox, 2013: https://stats.stackexchange.com/questions/67547/when-to-use-gamma-glms
#normality #normalDistribution #Γ #modelling #dataDev #AIDev #ML #AIEvaluation #logNormal
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In-class coin tosses: 16 participants, 18 tosses, and what felt like a relatively unusual distribution (after all, nobody with 10 heads). Goal of ever getting something really weird in class still not achieved :)
#teaching #coinTosses #statistics #normalDistribution -
Quick DISTRIBUTION FITTING with @LabPlot (a new development version) in five easy steps:
1. Select a data column in a spreadsheet.
2. Context menu > Plot Data > Histogram.
3. Select the histogram.
4. Context menu > Analysis > Fit your distribution of choice (e.g. Gaussian).
5. Tune the fitting properties (e.g. the Maximum Likelihood or Levenberg–Marquardt algorithm.#LabPlot #MaximumLikelihood #LevenbergMarquardt #DistributionFitting #Statistics #Gaussian #NormalDistribution
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Article in Hungarian about Hungarian language as a first language entrance exam for High School admission in Hungary.
TL/DR {clickbait}: No maximum score exam result yielded by the pupils.
Do you think NLP is smarter nowadays than an average teenager? (Hidden turing test singularity question)
