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Good for you for stating the assumptions properly that go into the CLT and for mentioning other stable distributions. I disagree about the Gaussian being the "

Good for you for stating the assumptions properly that go into the CLT and for mentioning other stable distributions. I disagree about the Gaussian being the "normal" case or the "one that usually matters". Finite variance is a big assumption and one that's routinely violated in practice. For those that are interested, Levy-stable distributions are the general class of convergent sums of random variables [0], synonymously called "fat-tailed" or "heavy-tailed" distributions and include Pareto [1] and the Cauchy distributions [2]. Is there an intuitive explanation for why the Wigner semicircular law is basically the "logarithm" the Gaussian in some respect? [0] https://en.wikipedia.org/wiki/L%C3%A9vy_distribution https://en.wikipedia.org/wiki/L%C3%A9vy_distribution [1] https://en.wikipedia.org/wiki/Pareto_distribution https://en.wikipedia.org/wiki/Pareto_distribution [2] https://en.wikipedia.org/wiki/Cauchy_distribution https://en.wikipedia.org/wiki/Cauchy_distribution

CrazyStat 2y ago
“Normal” in the context of the normal distribution actually derives from the technical meaning of normal as perpendicular, like the normal map in computer graphics. The linguistic overloading with normal in the sense of usual or ordinary is an unfortunate coincidence.
- abetusk 2y ago
  It looks like that story is apocryphal. There's a reddit question which refutes this idea [0] and provides some sources (which are paywalled) [1] [2]. That reddit question also has a source [3] that claims Galton used the term "normal" in the "standard model, pattern type" sense from the 1880s onwards: """ ... However in the 1880s he began using the term "normal" systematically: chapter 5 of his Natural Inheritance (1889) is entitled "Normal Variability" and Galton refers to the "normal curve of distributions" or simply the "normal curve." Galton does not explain why he uses the term "normal" but the sense of conforming to a norm ( = "A standard, model, pattern, type." (OED)) seems implied. """ Though I haven't confirmed, it looks like Gauss never used the term "normal" to denote orthogonality of the curve. Do you have a source? [0] reddit.com/r/statistics/comments/rvuj4r/q_why_did_karl_pearson_call_the_gaussian [1] https://www.google.co.uk/books/edition/Statistics_and_Public_Policy/TN3_d7ibo30C?hl=en&gbpv=0 https://www.google.co.uk/books/edition/Statistics_and_Public... [2] https://www.jstor.org/stable/2684625 https://www.jstor.org/stable/2684625 [3] https://condor.depaul.edu/ntiourir/NormalOrigin.htm https://condor.depaul.edu/ntiourir/NormalOrigin.htm

CrazyStat 2y ago

“Normal” in the context of the normal distribution actually derives from the technical meaning of normal as perpendicular, like the normal map in computer graphics. The linguistic overloading with normal in the sense of usual or ordinary is an unfortunate coincidence.

abetusk 2y ago
It looks like that story is apocryphal. There's a reddit question which refutes this idea [0] and provides some sources (which are paywalled) [1] [2]. That reddit question also has a source [3] that claims Galton used the term "normal" in the "standard model, pattern type" sense from the 1880s onwards: """ ... However in the 1880s he began using the term "normal" systematically: chapter 5 of his Natural Inheritance (1889) is entitled "Normal Variability" and Galton refers to the "normal curve of distributions" or simply the "normal curve." Galton does not explain why he uses the term "normal" but the sense of conforming to a norm ( = "A standard, model, pattern, type." (OED)) seems implied. """ Though I haven't confirmed, it looks like Gauss never used the term "normal" to denote orthogonality of the curve. Do you have a source? [0] reddit.com/r/statistics/comments/rvuj4r/q_why_did_karl_pearson_call_the_gaussian [1] https://www.google.co.uk/books/edition/Statistics_and_Public_Policy/TN3_d7ibo30C?hl=en&gbpv=0 https://www.google.co.uk/books/edition/Statistics_and_Public... [2] https://www.jstor.org/stable/2684625 https://www.jstor.org/stable/2684625 [3] https://condor.depaul.edu/ntiourir/NormalOrigin.htm https://condor.depaul.edu/ntiourir/NormalOrigin.htm