Simulating and Visualising the Central Limit Theorem
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Simulating and Visualising the Central Limit Theorem
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Re: Simulating and Visualising the Central Limit Theorem
#2Highly entertaining, here a little fun fact: there exist a generalisation of the central limit theorem for distributions without find out variance.
For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
Re: Simulating and Visualising the Central Limit Theorem
#3Highly entertaining, here a little fun fact: there exist a generalisation of the central limit theorem for distributions without find out variance. For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
Re: Simulating and Visualising the Central Limit Theorem
#4Highly entertaining, here a little fun fact: there exist a generalisation of the central limit theorem for distributions without find out variance. For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
3blue1brown has a great series of videos on the central limit theorem, and it makes me wish there were something similar covering the generalised form in a similar format. I have a textbook on my reading list that covers it, unfortunately I'm I can't seem to find it or the title right now. (edit: it's "The Fundamentals of Heavy Tails" by Nair, Wierman, and Zwart from 2022)
Do you have any good sources for the physics angle?
Re: Simulating and Visualising the Central Limit Theorem
#5Looking at the R code in this article, I'm having a hard time understanding the appeal of tidyverse.
Re: Simulating and Visualising the Central Limit Theorem
#6Looking at the R code in this article, I'm having a hard time understanding the appeal of tidyverse.
Why? The tidyverse is so readable, elegant, compositional, functional and declarative. It allows me to produce a lot more and higher quality than I could without it. ggplot2 is the best visualization software hands down, and dplyr leverages Unix’s famous point free programming style (that reduces the surface area for errors).
Re: Simulating and Visualising the Central Limit Theorem
#7Obligatory 3Blue1Brown reference
Re: Simulating and Visualising the Central Limit Theorem
#8Looking at the R code in this article, I'm having a hard time understanding the appeal of tidyverse.
the equivalent in any other language would be an ugly, unreadable, inconsistent mess.
Re: Simulating and Visualising the Central Limit Theorem
#9Highly entertaining, here a little fun fact: there exist a generalisation of the central limit theorem for distributions without find out variance. For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
I thought the rise of power laws in physics is predominantly attributed to Kesten's law concerning multiplicative processes, e.g. https://arxiv.org/pdf/cond-mat/9708231
Re: Simulating and Visualising the Central Limit Theorem
#10Highly entertaining, here a little fun fact: there exist a generalisation of the central limit theorem for distributions without find out variance. For some reasons this is much less known, also the implications are vast. Via the detour of stable distributions and limiting distributions, this generalised central limit theorem plays an important role in the rise of power laws in physics.
> find out
Finite?